AD-AIl 291 WRIGHT STATE UNIV DAYTON OHIO F/6 20/4PROBLEMS IN FORCED UNSTEADY FLUID MECHANICS. U)NOV Si N VIETS, M PIATT, M BALL. R J BETHKE AFOSR-78-3525

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letPRORBEJ IN FORCER, UNSTEADY' FLUID MECHANICS

BY

RmV ETS

WIgSTATE UIN!S

DTICrbOVEMBER 1981 SEL-ECT E)%

APPROVED FOR PUBLIC RELEASE.- DISTRIBUTION UN~LIMITED.

FLIGHT DYNAMICS LABORATORYAIR FORCE WRIGHT AERONAUTICAL LABORATODRIESWRIGHT-PATTERSON AIR FORCE BASE, OHIO 45433

82 0-1 - 021

FOREWARD

This report was prepared by Herman Viets, Michael Piatt,

Mont Ball, Richard Bethke and David Bougine of Wright State

University. The work was performed at Wright State University

under AFOSR Contract #78-3525. The project engineer was Capt George

Catalano with his work performed under work unit #2307N417 and covers

the period from November 1977 to October 1980.

This Technical Memorandum has been reviewed and is approved

for publication.

At ~ e g a ~!-RL C. KEEL jUS AFProject Engineer Chief, Aerodynamics and

Airframe Branch

AIR FORCE/56780/6 January 1982- 50 i//f

S E C U R IT Y C L A S S IF IC A T IO N O F T H IS P A G E (W h e n D a te E n te red ) , R E ADI N S T R U C T I O N SREPORT DOCUMENTATION PAGE EAD rNSTRUC'r[ONSBEFORE COMPLETING FORM

1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED

Problems in Forced Unsteady Fluid Mechanics Technical FinalI Nnv, 1q77_11 nirt 1RA6. PERFORMING ORG. REPORT NUbAER

7. AUTHOR(q) S. CONTRACT OR GRANT NUMBER(s)

Hermann Viets Mont BallMichael Piatt Richard J. Bethke

David Bougin69. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK

Wright State University AREA & WORK UNIT NUMBERS

Dayton, Ohio 45435 "

I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Air Force Office of Scientific Research NOV 1121.* 13. NUMBER OF PAGES

Bolling Air Force Base, DC 20332 231231 "

14. MONITORING AGENCY NAME & ADDRESS(II different from Controlling Office) IS. SECURITY CLASS. (of Shia report)

Flight Dynamics Laboratory/FXMWright-Patterson AFB, Ohio 45433 Unclassified

ISa. DECL ASSI FIC ATION/DOWN GRADINGSCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

1". DISTRIBUTION STATEMENT (of th abetract entlered in Block 20, if different fron Report)

18. SUPPLEMENTARY NOTES

19 KEY WORDS (Continue on reverse side ii necessary nd identify by block number)

unsteady flow time dependent flow wing rotorlets fluidics ramp vortex" orced flow flow structure diffuser

dump combustor

), BSTRACT (Continue on reverse aide If neceseary and identify by block number)

Forced unsteady fluid flows are examined from the point of view of positiveimplications of the time dependency. Particular problems examined in a forcedunsteady mode are jets, wind tunnels, wings, ramps and diffusers, dump combustorsand vortex structure. Two methods of forcing the flow are studied in detail,fluidic feedback and a cam-shaped rotor. The fluidic method produces an unsteadjet while the rotor acts as a time dependent vortex generator. Potential per-formance improvements with unsteady flow are evident in all of the flowsexamined.IDD I JAN ?, 3 EDITION OF I NOV 65 IS OBSOLETE

SECURITY CLASSIFICATION OF THIS PAGE (Wlen Data Entered)

il/V//

PROBLEMS IN

FORCED UNSTEADY FLUID MECHANICS

Hermann Viets*Michael Piatt**Mont Ball***Richard J. BqthketDavid Bougineit

Wright State UniversityDayton, Ohio 45435

*Professor**Research Assistant (presently with Systems and Applied Sciences,

Hampton, Va.)***Senior Research Technician

tAssociate ProfessorttResearch Assistant

vIv

TABLE OF CONTENTS

Section Page

I Introduction .......................................... I

1I Flowfield of an Unsteady Jet ...................... 2

by M. Platt and H. Viets

III Large Scale Structure in an Unsteady Jet ................... 9by H. Viets

IV fMultijet Flowfield as a Gust Tunnel....................... 16by H. Viets; M. Ball and MI. Platt,

V Linearized Unsteady Jet Analysis .......................... 23by H. Viets and M4. Platt

VI Forced Unsteady Flow Over a Wing .......................... 33by H. Viets; M. Ball and M. Piatt

V1I Unsteady Flow Over a Rearward Facing Ramp .................. 37by H. Viets; M4. Ball and M4. Piatt

VIII Induced Unsteady Flow in a Dump Comnbustor Geometry .......... 45by H. Viets and M. Piatt

IX Performance Potential of Unsteady Diffusers ................ 51by H. Viets; N. Ball and D. Bougine

X Details of the Flow Produced by the Rotor Vortex Generator . 57by H. Viets; M. Piatt and N. Ball

XI Data Analysis to Identify Large Scale Vortex Structures ... 64by R.J. Bethke and H. Viets

X1I References ............................................. 71

XIII Tables ................................................. 78

XIV Figures ................................................ 87

Accession For

~NTIS CPA&IDTIC T'B E

- t~Ion/ _

A,:il,'iil tY Codes

Arvii and/~or

Dict Special.

vii

LIST OF ILLUSTRATIONS

FIGURE PAGE

1 Schematic of a fluidically oscillating jet 87

2 Smoke flow visualization of the oscillating jet in a coflowingstream of 45.8% of the jet velocity 88

3 Smoke flow visualization of the oscillating jet in a coflowingstream of 28% of the jet velocity 89

4 Experimental setup 90

5a Time averaged velocity measurements in the oscillating jet,Uo=43 m/sec, w=12 Hz 91

5b Continued 92

5c Continued 93

5d Continued 94

5e Continued 95

6 Composite view of the time average oscillating Jet 96

7 Centerline and peak velocity decay for various frequencies inthe time averaged oscillating jet 97

8 Half width growth in the time averaged oscillating jet forvarious frequencies 98

9 Schematic of the electronic circuitry employed to conditionallysample the unsteady jet flowfield 99

10 Definition of the jet phase angle in terms of jet orientation 100

Ila Instantaneous velocity profiles in the oscillating jet at afrequency f=12 Hz and a phase angle e=900 101

lb Continued 102

llc Continued 103

lld Continued 104

viii

FIGURE PAGE

12a Composite of the instantaneous streamwise velocity profilesfor f=12 Hz, e=900 105

12b Transverse location of the maximum streamwise velocity withdistance downstream, 8=900 106

13a Instantaneous velocity profiles in the oscillating jet at a

frequency f=12 Hz and a phase angle 8=1800 107

13b Continued 108

13c Continued 109

14a Composite of the instantaneous velocity profiles for f=12 Hz,0=180 0 110

14b Transverse location of the maximum streamwise velocity withdistance downstream, 0=1800 111

15a Composite of the instantaneous velocity profiles forf=12 Hz, 8=270* 112

16a Instantaneous velocity decay for various phase angles anda frequency f=12 Hz 113

17 Typical velocity profiles from Simmons, Platzer and Smith,Reference 5 114

18 Smoke flow visualization of the oscillating jet in a coflowingstream of 28% of the jet velocity 115

19 Evolution of the jet surface waves 116

20a Jet velocity field at a frequency w=18 Hz and phase anglee=2700 117

20b Coherent structure of the jet seen in a moving coordinate

system 118

21 Anticipated vortex locations based on flow visualizationresults 119

22a Jet velocity field at a frequency of w=1 2 Hz and phase anglee=900 120

22b Coherent structure of Vortex B in a moving coordinate system 121

ix

FIGURE PAGE

23a Jet velocity field at a frequency of w=1 2 Hz and a phaseangle e=180° 122

23b Coherent structure of Vortex D in a moving coordinatesys tern 123

24a Jet velocity field at a frequency of w=12 Hz and a phase

angle of 0=2700 124

24b Coherent structure of Vortex F in a moving coordinate system 125

25 Effect of the vortex structure on the instantaneous jetvelocity decay 126

26 Schematic of mechanically controlled, fluidically activatednozzle 127

27 Schematic of jet contrulled gust tunnel 127

28 Geometry of the experimental subscale pilot gust tunnel 128

29 Flow visualization of the in-phase configuration in the upand down orientations 129

30 Schematic of conditional sampling electronics 130

31 Flowfield at R = 20 for the in phase configuration in theupward orientation 131

32 Flowfield at R = 20 for the in phase configuration in thedownward orientation 131

33 Decay of the velocity non-uniformity in the flowfield 132

34 Variation of the centerline transverse velocities with timeat several streamwise positions 133

35 Flowfield at X = 20 for the out of phase configuration and aninward orientation 134

36 Flowfield at X = 20 for the out of phase configuration and anoutward orientation 134

37 Variation of the centerline streamwise velocities with time atseveral streamwise positions 135

38 Streamwise velocities at various positions with a 450 phasebetween the nozzles and the upper nozzle in the upwardorientation 136

x

I'

FIGURE PAGE

39 Same nozzle configuration as Figure 13 but with the upper nozzlein the downward orientation. 137

40 Flow visualization of the in-phase gust flow over an airfoilat various phase angles. 138

40 Continued 139

41 Schematic of the vibrated jet studied by McCromack, Cochranand Crane. 29 140

42 Flapping jet with angular time variation at the exit studiedby Viets et al.3,A5 and Platzer et al. 10 140

43 Jet with time dependent mass flow studied by Binder and

Favre-marinet and Curtet and Girad.2 141

44 Initial and downstream velocity profiles 141

45 Fluidically Controlled Jet Nozzle Design 142

46 Half width growth dependent upon oscillation frequency 143

47 Flow over a wavy wall 144

48 Geometry and Flowfield of an Oscillating Airfoil 145

49 Hydrogen Bubble Flow Visualization of the Field Around anOscillating Airfoil (from McAllister and Carr, Ref. 37A) 146

50 Vortex Generation by an Embedded Rotor 147

51 Airfoil and Rotor Geometry 148

52 Airfoil Mounted for Low Speed Wind Tunnel 149

53 Vortex Structure Behind the Rotor on a Flat Plate 150

54 Flow Visualization of the Flow Structure at a = 200. 151

55 Effect of the Rotor Speed on the Streamline pattern overthe Airfoil 152

56 Instantaneous Vortex Structure on the Airfoil fora= 20', w = 1000 rpm. 153

57 Pressure Variation with Rotor Speed for Three Angles of Attack 154

xi

6 , _ X = Q '-:'" ... . . .. 'T.. .......P L ...- - -' ",'.,.,,. - 2 ,_-

-r_ _a- : -.--,,. ...

r1

FIGURE PAGE

58 Pressure Variation with Angle of Attack with/withoutActivated Rotor 155

59a Unsteady Ramp Flow Configuration 156

59b Tunnel Geometry 156

60 Pressure Distribution on the Ramp for e = 200 157

61 Pressure Distribution on the Ramp for 8 = 28* 158

62 Pressure Distribution on the Ramp for e = 300 159

63 Time averaged Flow for 6 = 280 160

64 Instantaneous Streakline Photographs for Various RotorSpeeds at e = 280 161

64 Continued 162

65 Schematic of a three dimensional rotor geometry (Tapered rotor) 163

66 Comparison between rotor motion in the upstream (+) anddownstream (-) directions for w = 1000 and 2500 rpm, and atapered rotor 164

67 Same as Figure 66 for w = 4000 and 5000 rpm 165

68 Presure rise down the ramp for + 1000 rpm and a tapered rotor 166

69 Pressure rise down the ramp for + 5000 rpm and a tapered rotor 167

70 Streaklines in the ramp flowfield for a tapered rotor moving inthe counter-clockwise (+) and clockwise (-) directions 168

71 Same as Figure 70 for higher rotor speeds 169

72 Ramjet Combustor Flowfield 170

73 Experimental Geometry and Rotor Flowfield 171

* 74 Streamline Shapes for Various Rotor Speeds, = 1/3 172

75 Instantaneous Streaklines for 0 = , I = 1/3 173

76 Streaklines at Three Different Instants, L = 2500 rpm,Ii-1/3 174

77 Streaklines for w = 5000 rpm, F - 1/3 175

78 Streamline Shapes for Various Rotor Speeds, ! = 1 176

Xii

FIGURE PAGE

79 Streaklines for Various Rotor Speeds, 1 = 177

80 Pressure Distribution Downstream of the Dump Station;h = 1/3, Various Rotor Speeds 178

81 Pressure Distributions Downstream of the Dump Station;= 2/3, Various Rotor Speeds 179

82 Pressure Distributions Downstream of the Dump Station;1, Various Rotor Speeds 180

83 Effect of Rotation Direction on Pressure Distributions 181

84 Effect of Rotor Geometry as a Passive Trip 182

85 In phase and out of phase rotor orientation 183

86 Vortex produced near the corner of the diffuser 184

87 Multiple vortices produced in the diffuser by increasingthe speed of the rotor 185

88 Streaklines produced for 0 = 8' and 120 showing separationat 120 and time averaged velocity profiles taken at thediffuser exit verify the separation 186

89 Longer exposure streamline photographs for 2E = 30* . (a).Separation at the bottome for W = 0 (b). Weaker separation atthe top for w = 11.84 (both in phase) 187

90 Pressure rise through the diffuser for 2e = 16 and variousrotor speeds, out of phase 188

91 Pressure rise for larger angle diffuser, 2o = 240, out of phase 189

92 Pressure rise for 20 = 300,out of phase 190

93 Diffuser performance for rotors set in phase and 20 = 240,in phase rotors 191

94 In phase pressure rise for 20 = 300, and rotors in phase 192

95 Streakline photographs of the diffuser flow at differentphase positions with superimposed instantaneous velocityprofiles 193

Lim )(i ii

FIGURE PAGE

96 Streakline photographs for a larger diffuser angle and forthe out of phase rotor orientation 194

97 The presence of a counter-clockwise vortex near the upperwall or a clockwise vortex near the lower wall leads toinstantaneous velocity changes in the streamwise (u') andtransverse (v') directions 195

98 Velocity difference between the presence of a vortex pairb = 1800) and no vortex (o = 90) 196

99 The velocity changes due to the presence of a single vortexin the out of phase condition. The profiles are those inFigure 96 (b) and (d) 197

100 Schematic of the vortex flow generated by a cam shaped rotor 198

101 Flow visualization of vortex structure produced by thevortex generator with w = 3000 rpm 199

102 Flow visualization of vortex structure produced by thevortex generator with w = -3000 rpm 200

103 Flow visualization of vortex structure produced by thevortex generator with w = 2000 rpm 201

104 Flow visualization of vortex structure produced by thevortex generator with w = -2000 rpm 202

105 Flow visualization of vortex structure produced by thevortex generator with w = 1000 rpm 203

106 Flow visualization of vortex structure produced by the vortex

generator with w = -1000 rpm 204

107 Schematic of conditioned sampling apparatus 205

108a Instantaneous velocity field with the rotor fully extended inthe e = 0' position 206

108b Identification of a vortex structure in a reference framemoving at 11.5 m/sec 207

109a Instantaneous velocity field with the rotor in the e = 1200position 208

109b Identification of a vortex structure in a reference framemoving at 11.8 m/sec 209

xiv

FIGURE PAGE

109c More detail of the flow near the rotor with 0 = 1200 210

109d Identification of a vortex structure in the flowfield ofFigure 109c 211

l1a Instantaneous velocity field with the rotor in the e = 2400orientation 212

lOb Identification of a vortex structure in the flowfield ofFigure llOa at x = 4.5, y 2.0 213

llOc Identification of a vortex structure in the flowfield ofFigure llOa at x = 13.0, y = 5.75. 214

111 Trajectory of the vortpx center as it moves downstream 215

112 Influence of the vortex on the streamwise velocity profile 216

113a Spatial vortex existing on the axis 217

113b Transformation of the vortex of Figure 113a 218

114a Vortex shifted to an off axis location. Center shifteddown by 50 units and right by 64 units from the upper leftdata point. 219

114b Schematic of phase angle shift 220

115 Rotational flow with a constant magnitude velocity 221

116a Superimposed vortex on a parabolic translational flow 222

116b Translational velocity component of the flowfield ofFigure 5a 222

116c Flowfield in the moving coordinate system 223

117 Instantaneous velocity structure of an oscillating jet 224

118 Flow structure in a reference frame moving with the velocityat the point identified as the vortex center 225

119 Generated velocity field containing two vortices 226

120a Schematic of two vortices in the physical plane 227

120b Schematic of the transformed plane of vortex number 1 inFigure 120a showing magnitudes and phase angle changes due toshift of vortex center location 228

'('

..... --- - - - -- * _- -: * . - ... .... . ... .. .. . .. . .' ". . . - -. ... . -- : ': . ... . . , ,. :

FIGURE PAGE

120c Schematic of the transformed plane of vortex number 2 inFigure 120a, showing magnitudes and phase angle changes dueto shift of vortex center location 228

121 Instantaneous velocity field generated by the rotor 229

122a The upstream vortex in a coordinate frame moving with itscenter 230

122b The downstream vortex in a coordinate frame moving withits center 231

qvi

SECTION I

INTRODUCTION

The historical evolution of fluid mechanics has generally emphasized

the elimination of unsteady flows as undesirable. Two examples are the

attempts to eliminate inlet buzz and wing flutter. There are, however,

situations in which unsteady flows can have performance advantages and

some have led to application as in the case of pulsed combustion "buzz

bombs" of the 1940's.

More recently, the potential advantages of unsteady flow have been

pursued in a variety of applications. The rates at which jets mix with

their surroundings have been increased by introducing a time dependency

into the jets by acoustic,1 mechanical2 or fluidic 3 means. In the boundary

layer, mechanically activated unsteady wall jets have been shown to achieve

the same performance as steady jets with only one half the mass flow required.4

Pulsed combustion gas furnaces are currently being investigated5 with an

eye to improving efficiency.

In the animal world, unsteady flow is rather common and its advantages

are chronicled by Lighthill.6 The question of flapping wing flight is

currently being investigated to determine performance effects of the time

dependency 7 while in the boundary layer the moving surface waves on porpoises

may lead to drag reduction.8

The above examples, as well as many others, indicate that unsteady flow

is not always detrimental to performance but is actually advantageous in

particular cases. Thus, the objective of the present investigation is to

examine unsteady flow from a positive point of view and to identify situations

where the time dependency is an asset.

The earlier sections deal with unsteady flow in jets and the resulting

large scale flow structures. Later sections are concerned with unsteady flowfields

produced by a mechanical rotor which creates transverse vortices. In each case

some potential advantages are discussed.

17

SECTION II

FLOWFIELD OF AN UNSTEADY JET

1. Background

Various methods have been proposed to induce unsteady flow in jets.1 "4 ,9,10

In general, the objective is to affect the rate at which the jet mixes with its

surroundings. The particular jet nozzle design employed in the present study

is described in Reference 3 and consists of a modified fluidic element with

a feedback mechanism.

The nozzle design and the jet it produces are shown in Figure 1. In this

case the feedback loop is built around the nozzle body in order to minimize

its influence on any external flow. The jet oscillates from side to side in

a quasi-sinusoidal fashion and rapidly mixes with the coflowing stream or

the ambient fluid. The oscillation is produced without the need for moving

parts.

2. Flow Visualization

The fluidic nozzle shown in Figure 1 is mounted in a smoke tunnel to

illustrate the dynamic interaction between the jet and the surrounding fluid.

The smoke is produced by allowing kerosene to drip on an inclined resistance

heater. The kerosene vapor is forced out through tubes and then entrained

into the open circuit smoke tunnel inlet. The instantaneous streakline

pattern is shown in Figure 2 for a coflowing stream to jet velocity ratio of

.46 and a frequency of 30.5 Hz. A sinusoidal-like structure may be seen, but

the interaction between the jet and coflowing stream is rather weak.

Reducing the coflowing stream to 28% of the jet velocity while holding the

jet velocity (and hence the frequency) constant results in a greatly increased

interaction between the jet and external flow as may be seen in Figure 3. The

shear forces between the two flows have increased and produce an apparent vortex

structure which is swept downstream. The vortex formation enhances the mixing

due to the presence of the large scale structures.

3. Time Average Measurements

The fluidic nozzle is mounted between two Plexiglas sheets to minimize the

three dimensional effects, as shown in Figure 4. A hot wire probe is mounted on

a motorized traversing mechanism which also drives a potentiometer to indicatethe position of the probe. A Flow Corporation (now Datametrics, Inc.) Model 900

2

- .... : "'- - -- :- - : """ -" ... ..... " -i.-- -- '

.. . ,, , .

two channel constant temperature hot wire anemometer is employed along with an

X probe geometry. A pair of Thermo Systems, Inc., model 1072 linearizers

multiply the signal from each wire by a fourth order polynomial whose required

coefficients have been determined by calibration. Thus the output voltage of

each varies linearly with velocity. The appropriate geometrical relationships

(based on the orientation of wires) then yield the x and y velocity components

which are then simply filtered to eliminate the A.C. and leave only the D.C.

or time average signal. The velocity and the probe position are then plotted

on a Hewlett-Packard Model 2FA X-Y plotter. The circuitry required to obtain

the instantaneous velocity distribution will be discussed in the following

subsection.

A series of velocity profiles depicting the time averaged flowfield

structure is shown in Figure 5. The velocity distribution at a point close

to the nozzle exit (i = .20) is presented in Figure 5a, both for the streamwise

(u) and transverse (v) components. The frequency is 12 Hz and the velocity

profiles are similar to those found in steady jets. The transverse velocity

(v) indicates that far from the jet, entrainment causes an inflow toward the

jet which increases as the jet is approached. The inflow goes to zero at the

jet's edge and within the jet the transverse flow is outward due to the spread-

ing of the jet itself.

Farther downstream at i = 6.(i = x/D where D is the nozzle throat dimension)the character of the average flow changes considerably as shown in Figure 5b.

The streamnwise profile has developed a double peak. It appears that this

phenomenon is due to the quasi-sinusoidal oscillation characteristic of the

particular nozzle design. The jet spends more time in the extreme angular

positions than it does making the transition from side to side. Examination

of the transverse velocity profile shows that flow is moving from the center

valley toward the peaks, with additional entrainment of ambient fluid from outside

the jet.

At the streamwise distance 10 diameters downstream the u velocity profile

still exhibits a double peak as shown in Figure 5c. An indication of the

interaction between the two peaks is given by the corresponding transverse

velocity profile which has an extensive flat region in the center. Thus the

transverse velocity between the peaks is very small. If the two peaks are

considered to be individual steady jets for the sake of analysis, their effect

3

on each other is simply to limit the entrainment on their common side. Each

jet would then behave as though there were an invicid wall on that side.

Still farther downstream at R = 14, the transverse velocity profile shows

that now flow is moving from the peaks into the center valley filling that

valley as shown in Figure 5d. Figure 5e shows the time averaged u and v

velocity profiles at 22 diameters downstream. The streamwise velocity has

returned to a single peak profile. The transverse velocity has also returned

to a form typical of a steady jet which is not rapidly growing. That is,

the flow within the jet itself is roughly parallel so no outflow appears but

only inflow produced by entrainment.

A compc ite picture of the streamwise Velocity profiles at their relative

downstream positions for a frequency of 12Hz is shown in Figure 6. The behavior

of the time averaged velocity distribution can be described in a three stepprocess. Near the nozzle exit the double peak profiles are formed and diverge

from each other, entraining fluid from outside the jet and from the center

valley. Farther downstream, the velocity in the valley reaches a minimum.The transverse flow begins to move toward the jet centerline, filling the valley

while entraining fluid from outside the jet. The final process is the

development of a typical two dimensional jet velocity profile with a single

peak on the centerline.

This behavior was observed at four different frequencies from 4 Hz to

18 Hz. Figure 7 depicts the time averaged centerline velocity decay for

frequencies of 4, 8, 12 and 18 Hz respectively. Their corresponding half

width growths are shown in Figure 8. The centerline velocity is nondimensionalized

with respect to the time averaged exit velocity. The half width, defined as

the distance between the centerline and the position of half the reference

velocity, is nondimenslonalized with half the nozzle exit dimension.

As shown in Figures 5 and 6, the maximum velocity is not always at the

jet centerline. In steady jet problems, the centerline velocity is generally

used as the reference velocity for the half width growth and velocity decay

determination. However, the peak velocity may be more indicative of the mixing

rate so both are shown. For the same reason, both the values of half widths

based on the peak and valley velocities are presented in Figure 8. Of course,

the two sets of curves coalasce when the double peak disappears.

The time averaged velocity decays (Figure 7) and half width growths (Figure8) are rather weak functions of frequency, if they are based on the peak velocity

4

at each streamwise position. However, based on the centerline velocity, both

the velocity decay and the jet growth are strong functions of oscillation

frequency. At low frequencies, the centerline velocity decays very rapidly

and then rises somewhat under the influence of the double jet peaks. At

higher frequencies, the decay is much weaker and leads to the conclusion

that at very high frequencies, it is possible that only a single velocity

peak appears.

The use of the centerline velocity as a reference also leads to a

frequency variation in the half width growth. The difference between the

two computed half widths is greatest at low frequencies and has almost

disappeared at a frequency of 18 Hz.

4. Instantaneous Velocity Measurements

a. Experimental Apparatus

The objective of this portion of the experiment is to produce velocity

profiles to indicate the unsteady flowfield at a single instant. In

order to achieve this, the hot wire must sample at precise times and

these samples must be taken when the jet itself is in a known orientation.

Thus the sampling of the hot wire circuit must be conditioned by the

knowledge of the overall jet orientation. The jet orientation is

determined by an additional hot wire probe referred to as a trigger.

A schematic of the circuitry is shown in Figure 9.

The triggering probe employs the simplest hot wire circuit, a

power supply in series with a large resistor and the wire. The hot wire

resistance is relatively small so that the current passing through

it is essentially constant. The wire is placed in a fixed orientation

near the jet exit so that it is periodically exposed to the jet flow.

The periodic signal is amplified and band pass filtered so that only the

fundamental jet frequency is present. The resulting signal is passed

through a zero crossing detector which then produces a square wave which

is correlated with the jet orientation.

Since one wishes to sample the flowfield with the jet in several

different (but fixed) orientations, a variable phase shifter is employed.

The signal then can be used as a trigger for the jet in various fixed

positions. After suppressing the D.C. voltage produced by the phase

shifter, the signal is amplified and fed to a Schmitt trigger which again

5

produces a square wave. The square wave is differentiated and clipped

to yield a spike of 50 ps width. Finally, this spike is the input to a

sample and hold amplifier along with the analog signal from the hot wire

anemometer. The output is the conditionally sampled hot wire data where

the timing of the sample is determined by the triggering circuit. Thus

the circuit only samples when the jet is in a given fixed position and

the signal is output on an X-Y plotter versus the vertical position

determined from a potentiometer. The result then is a velocity profile

at an instant when the jet is in a given orientation.

b. Orientation 900

A sketch of the jet orientations defined in the present case is

shown in Figure 10. The first orientation to be discussed here is the

900 case where the jet at the origin is instantaneously pointing straight

downstream and moving down between an upward and downward orientation.

The frequency is 12 Hz.

The instantaneous velocity distributions at R = .20 is shown in

Figure ila. The streamwise component is a single peak as might be

expected and is almost symmetrically oriented with respect to the

streamwise axis. The instantaneous v velocity component is not at all

symmetrical, however, and gives the first indication of the time dependency

involved in the flow. Approaching the jet from below, there is an upward

component due to the entrainment into the jet. Within the lower part of

the jet, v is downward because the lower part of the jet is spreading in

that direction. The upper half of the jet has a rather large upward

velocity component which is probably due partly to spreading in that

direction and partly to a small asymmetry which can also be seen in the

u component (with some difficulty).

At a streamwise position i = 6, (see Figure llb) the asymmetry of the

time dependency is clear. Here even the u velocity is asymmetrical with

respect to the centerline and within the jet the v velocity is strongly

upward. The reason for this may be seen in the schematic of Figure 12

showing the jet in the instantaneous 90' position and the quasi-sinusoidal

wave downstream. At R = 14, the asymmetry in the u velocity is rather

strong (Figure llc) and the position of the jet can be determined almost

as well by the maximum v velocity as the maximum u component. The slower

decay of the u component below the jet (as opposed to above) is due to the

6

- --- ~-

setting up a significant entrainment flow as may be seen in the strong

upward flow of the v component below the jet.

The effect gets even stronger by i = 22, but by i = 30 the flow is

rather diffuse, Figure lid. The fact that the u component reaches its

maximum below the nominal centerline may be seen and is borne out by the

fact that the v component is downward. A plot of the lateral position of

maximum streamwise velocity is presented in Figure 12b and confirms the

schematic of Figure 12a.

c. Orientation 1800

At an orientation of 1800, the jet is in the extreme downward position,

as seen in Figure 10. This is evident in Figure 13a where the u component

is skewed to a position below the centerline and the v component indicates

entrainment into the jet from above and below while the v velocity within

the jet is in a downward direction.

By R = 6 (Figure 13b), the streamwise flow is highly asymmetric and,

except for some enir-Aned low rather far below the jet, in a very strongly

downward orientation. At an R = 18, the jet orientation is upward as may

be seen in the t, zompof ent peak above the axis and the upward component in

v (Figure 13c). The full flowfield at the instant the exit jet is in the

down position is s)wwn in Figure 14, along with the plot of the maximum

velocity position as a function of streamwise distance. The position of the

unsteady jet may still be clearly seen at R = 30 and to some extent at

x= 40.

d. Orientation 2700

At an orientation of 2700 the jet is in a horizontal position, moving

up between a downward and upward orientation. Similar behavior is observed

and in fact the velocity profiles are almost the same as an inverted version

of those obtained at the 900 orientation. The composite picture of the

streamwise velocity profiles and the corresponding plot of the transverse

coordinate of maximum streamwise velocity are shown in Figure 15.

The downstream velocity distribution at any instant reflects, of course,

the past history of the jet. At an oscillation frequency of 12 Hz it

appears that approximately 3/4 of a wave has traveled downstream in 30 jet

diameters. Each of the phase angles investigated show the maximum

7

streamwise velocity at R = 30 to be located at a y coordinate corresponding

to a phase shift of roughly 2700 from the jet orientation at the nozzle exit.

e. Velocity Decay

The time averaged jet velocity decay has been discussed in relation to

Figure 7 for various oscillation frequencies. The corresponding instantaneous

streamwise velocity decays are shown in Figure 16 for both the 12 and 18 Hz

frequencies. Thus the data represents the spacial decay of streamwise

velocity within an existing jet at a single instant of time. The velocities

are all nondimensionalized with respect to the instantaneous exit velocity.

The velocity decay rates are much greater than the decay rate for a

steady two dimensional jet, also shown in Figure 16. However, by comparison

with Figure 7, it may be seen that the instantaneous jet decays more slowly

than the time averaged unsteady jet. This is to be expected since the time

averaged jet mixes very rapidly in part by the actual distribution of the

flow by the flapping process.

The streamwise velocity decay for both a steady and a time average jet

is a monotonically decreasing function. However, for the instantaneous jet,

it is evident that there exists a small peak in the otherwise generally

decaying function. Recent evidence leads to the conclusion that these peaks

are associated with a large scale unsteady structure in the oscillating jet.

This structure will be discussed in the following section.

5. Discussion

The most relevant comparison with existing experimental data is with that due

to Simmons, Platzer and Smith s who studied a mechanically oscillating plane jet.

The oscillation was forced by actually rotating the nozzle exit through small

angles.

A basic result of the Simmons, et al. 5 paper is that the low frequency unsteady

jet may be treated in a quasi-steady manner. That is, the velocity profiles shown

in Figure 17 (from Ref. 5) are essentially symmetrical about their maximum

velocity positions and the unsteady jet flap structure is similar to a plane

jet issuing into a coflowing stream. Thus the time dependency is overpowered by

the quasi-steady structure set up so quickly about the jet (relative to the

oscillation) that the jet acts as though it were a steady jet in that orientation.

The present results do not indicate such a situation. The dynamics of the jet

motion are clearly important in the instantaneous structure since there is no

8

similarity in the streamwise velocity profiles and indeed a very strong change

in the character of the transverse velocities (which were not measured in Ref. 5).

At least two reasons for the discrepancy can be advanced. The first is the

difference in the reduced frequency of the oscillations; that is, the speed of

the oscillation relative to the experimental parameters, specifically the jet

velocity and a scale length. If the reduced frequency is defined as

Ujet/D

where w = forcing frequency, Ujet is the jet exit velocity and D the jet exit

scale, then in the Simmons, et al. 5 results, this parameter has a value of from

.00824 to .0058. In the present experiments the values are an order of magnitude

higher, ranging from .0081 to .0363. The effect is primarily due to a reduction

of the jet velocity and an increase in the jet exit scale.

An even stronger effect on the importance of unsteady flow in the jet mixing

is the presence of a coflowing external stream. It can be clearly seen in

Figures 2 and 3 that the presence of a coflowing stream can have a substantial

influence on not only the rate of jet spread but also on the scale of the time

dependency. Therefore, it appears likely that a reduction of coflowing stream

speed will result in an increased mixing rate due to the unsteadiness of the flow.

SECTION III

LARGE SCALE STRUCTURE IN AN UNSTEADY JET

1. Background

The existence of coherent structures in turbulent shear flows"' has greatly

complicated the task of modelling these flows. Since the use of local transport

properties does not appear to be adequate, future descriptions of turbulent flows

will probably rely more heavily on phenomenalogical models. The flow may then be

based on some observations of its structure. A very simple example would be to

model the coherent large scale structure of a free jet by a number of vortices

* being convected downstream in a jet without a large scale structure. Of course,

other difficulties arise; in particular, the questions of how this structure is

initially formed1 2 and the geometrical relationships involved.1 3

The motivation, then, for studying unsteady flows is not only due to their own

usefulness but also as a guide to the modelling of "steady" flows. In particular,

9

the purpose of the present section is twofold:

1. Demonstrate some positive aspects of unsteady flow.

2. Produce flows in which the origin of the coherent structureis readily identifiable, thereby perhaps simplifying themodelling task.

2. Qualitative Structure

The introduction of a time dependency into free jet flows has been accomplished

by various methods including mechanical, 2 acoustic'and fluidic 3 means. The fluidic

method is considered here and consists of a feedback circuit which produces a

jet which flaps from side to side.3 The main advantage of this system (as with

all the unsteady jets) is a more rapid mixing of the jet with the surrounding

fluid. The unsteady jet nozzle employed here is shown in Figure 1 and described

in detail in Ref. 3. The feedback loop is incorporated into the nozzle body to

minimize the interference with the coflowing stream.

The large scale coherent structure in free shear layers, as demonstrated by

Roshko and Brown 14 (see also Ref. 11), is difficult to model due to the lack

of detailed understanding of its origin. Although it is clear that the large

scale structure is born in the turbulent shear layer, its growth and geometrical

spacing have not been predicted analytically. However, it has been shown that

the scale must increase with streamwise distance12 and that the spacing also

increases by the amalgamation of adjoining structures. 13 A simpler problem,

from the modelling point of view, is the unsteady flow in which the origin of

the largest scale structure is more evident.

The large scale structure in the oscillating free turbulent jet is shown

in Figure 2. The flow structure is visualized by entraining kerosine smoke

into the open circuit low speed wind tunnel. The nozzle exit is at the left

and the flow is from left to right. The ratio of the coflowing stream to

nozzle exit velocity is .458. Although the jet is highly turbulent, the

coflowing stream turbulence is low enough to produce a visible study of the

entrainment into a unsteady Jet. With such a relatively high coflowing stream,

the amplitude of the jet oscillation is not large but the appearance of the

large scale structure is evident at various streamwise positions. At position

A the large scale structure can only be seen with some difficulty. By position

B, the structure is a clearly defined mass of fluid which is rotating in

the clockwise sense. The disturbance has grown quite large by streamwise

position C.

10

If the coflowing stream velocity is reduced to 28% of the jet exit velocity,

the magnitude of the large scale structure is increased significantly as shown

in Figure 3. Now the large scale structure is very evident at position A and the

structure at position C has grown to the extent that it dominates the jet

flow. Perhaps even more interesting is the structure at position B where the

turbulent flow is clearly rotating in a clockwise sense. Since the flow is

unsteady, the smokelines are not streamlines but streaklines so the interpre-

tation is less straight forward. However it appears that of the two streaklines

at position B, the lower one is deflected around the large scale structure

while the upper streakline is being entrained into the turbulent large scale

structure which is the jet. This interpretation is verified by observing the

oscillation with a strobe light which is tuned so that there is a small frequency

difference between the strobe frequency and the jet oscillation frequency. Then

the jet appears to flap in slow motion and the rotational motion may be clearly

seen. Thus, the large scale unsteady structure behaves in the same way as the

large scale undriven flow structure described by Roshkoll and entrains fluid

on the upstream side. A similar entrainment pattern for the turbulent wake

has been found by Bevilaqua and Lykoudis.15 The effect may be seen for the

larger structure at position C in Figure 18 where the turbulent flow is

entraining the coflowing stream on the upstream side of the large scale structure.

Returning now to Figure 2, it may be seen that the turbulent jet produces a

large scale structure of its own in addition to that produced by the time

dependency. The peaks of smoke on the streaklines closest to the nominal jet

centerline all point in a downstream sense, in the same way as those produced

by the time dependent structure (position C of Figure 18). Thus, the turbulentunsteady jet produces a "steady" and an unsteady large scale structure but the

unsteady portion appears to dominate the flowfield. This may be somewhat

analogous to the domination of the large scale structure over the fine scale

turbulence in the "steady" jet. Here "steady" is employed to indicate that the

jet is steady in the gross view, while there is unsteadiness associated with

the turbulence structure.

Both the "steady" and unsteady large scale structures appear to arise

through the same, or at least a similar, mechanism. The jet produces a

perturbation on its surface. This bulge in the surface grows into a rotating

mass of fluid with a vortex-like structure. In the "steady" case the origin

and spacing of the structure is not fully understood. In the unsteady case, the

..J 11

bulges are produced at a known position and frequency and therefore may be

easier to analyze.

3. Modelling the unsteady jet

To understand the production of the large scale unsteady structure in the

unsteady jet, it is useful to construct a very simple phenomonalogical model of

the process. It appears that the growth of the unsteady structure greatly

resembles the growth and subsequent breaking of a water wave. This may be seen

by examining three positions of the developing large scale structure shown

schematically in Figure 19a, where u.(x) and uc are the jet and coflowing stream

velocities, respectively. The original deformation of the free jet surface is

a relatively small amplitude wave. This wave travels downstream (left to

right) at a velocity uwave such that uc < Uwave < u. Therefore the wave is

in a shear flow which causes it to curl in a counter-clockwise direction and

entrain fluid into itself. Even without shear, it can be shown that the top

of the wave outruns the bottom and curling results. 16 After the curling up is

completed, the vortex-like structure continues to entrain fluid. The photographs

of Figure l9b are taken from positions A, 2 & C of Figure 3, where position B

has been printed as it would appear on the upper surface of the jet. They

clearly verify the schematics of Figure 19a.

If one considers a breaking water wave, the schematic of Figure 19a

corresponds to the wave shape at three instants of time, however with the wave

traveling from right to left. Position A is the earliest swelling of wave. As

the wave travels to the left, its forward face steepens and finally breaks as

shown at position B. By position C the wave has broken and resembles a vortex

like structure. The energy of the breaking wave is transformed partially into

turbulence, which is eventually dissipated as heat, and partially serves to

energize the undertow16 which is the jet velocity itself in the present analogy.

The analogy is incomplete, however, because the water wave is driven by gravity

and somewhat by viscous effects while the jet structure is entirely a viscous

phenomenon. In spite of this, once the viscosity has created a vortex sheet at

the interface, the deformation of this sheet may be modelled inviscidly12 ,1 3

with considerable success.

The main point then is not that the steady and unsteady flow structures are

the same but rather that they may have similar origins. As the unsteady structure

grows from a large amplitude surface wave, so that steady structure may grow from

a small amplitude surface wave.

12

S- ~ - - -----

4. Quantitative ConfirmationThe unsteady fluldically controlled jet was examined in some detail by employing

a hot wire anemometer along with conditioned sampling of the data to reveal the

time dependent character of the flowfleld. The jet was positioned between twoPlexiglas sheets to attempt to minimize the three dimensionality of the field, as

shown in Figure t. The hot wire anemometer was driven through the flowfieldby a motorized traversing mechanism which also turns a potentiometer, so the

probe position is known at any time.The data required are the velocities in the jet at a specific instant of time

(or alternately, at a specific point in the oscillation cycle, since the

oscillation is repeatable). The conditioned sampling method is shown schematicallyin Figure 9. A third hot wire anemometer is employed to indicate the position

of the jet since its signal is maximized when the jet is in the upward orientation.As discussed in Section II, the velocity data is only accepted and recorded when

the third hot wire indicates the jet is in the required instantaneous orientation.The data obtained by the above technique have been reported in some detail in

Reference 17. The aim here is to investigate quantitatively the existance oflarge scale coherent structure in the jet as appears to be evident in the flow

visualization experiments described above. Looking back at the schematic of the

unsteady jet field in Figure 1, a growing sinusoidal wave traveling downstream,where should one look for the existance of the vortex structure observed in the

smoke photographs? The question is answered by another look at the model of

Figure 19. As the bulge of the jet flow curls up to create a vortex structure,it necessarily does so by breaking toward the upstream direction (as driven

by the slower coflowing stream or ambient fluid). Thus the vwtex produced would

be expected to exist at a position somewhat upstream of the ir.ial jet b Ige,

which in this case is the extreme off axis position of the instantaneous jet

centerline.A portion of the jet flowfield, for the case of a frequency of 18 Hz and an

extreme downward orientation of the jet at the nozzle exit, is shown in Figure 20a.

The lengths of the arrows are proportion to the local velocity and the anglesare determined from the measured axial and transverse velocities. The instantaneous

jet centerline is also shown, from which it may be estimated that if a vortexis present, it should be centered roughly between 16 and 22 jet diameters

downstream. No vortex-like structure is evident in this region.

13

Several investigators have shown, however, that in order to see the coherent

motion of a group of particles, the observer must be travelling with the velocity

of the center of mass of those particles. Probably the first examination of

this effect was made by Prandtl18 who photographed a boundary layer by travelling

at various speeds relative to the flow. Each photograph then revealed a different

coherent structure.

In order to see the structure in the flowfield of Figure 20a., a nominal

velocity of the vortex center is assumed and that streamwise velocity subtracted

from each of the data points in the field. The result is shown in Figure 20b

and clearly shows a vortex located in the very region where one would expect it

based on the flow visualization results presented above.

Based on the phenominological model of Figure 19 and the quantitative

results of Figure 20 one can then make more predictions of the location of

large coherent vortices in a family of instantaneous jets as shown in Figure 21.

The 12 Hz frequency jet is shown for three phase angles, 900, 1800 and 2700 or

horizontal (sweeping top to bottom), extreme downward or horizontal (sweeping

bottom to top) orientation, respectively. The centerline positions of the jets

are based on quantitative results. The vortices are drawn in the positions where

they might be expected to be found based on the previous results.

Searching at the three positions closest to the nozzle exit, A, C and E leads

to the conclusion that coherent vortices do not exist at those positions. This

is, however, entirely consistent with the model proposed in Figure 5. It is

clear from the flow visualization experiments that it takes some time (or equiva-

lently, distance) for the bulge on the jet to curl up into a coherent structure.

The positions near the jet exit simply have not allowed enough time (or distance)

for this process to take place.

Looking for the vortex B, the local jet velocity field is shown in Figure

22a. Assuming the vortex center to exist at roughly x = 22 and subtracting the

streamwise velocity at that point results in the Figure 22b where the vortex

structure is evident. It should be emphasized, of course, that the local

structure depends upon the velocity of the observer, so subtracting a somewhat

different velocity will result in a somewhat different appearance of the vortex.

However, the important fact that the vortex is there is clear in any case.

The local velocity field for a phase angle of o = 1800 is shown in Figure 23a.

Again no vortex structure is seen until the flow is observed from a moving

coordinate system as shown in Figure 23b. The vortex appears to be centered

14

approximately at 1 10. Looking back at the schematic of Figure 21, it may

be seen that vortices A, D and F are really one and the same vortex at successive

times. Thus an indication of the translational speed of the vortex can be

obtained by locating the vortex F, having already found vortex D.

The jet flowfield in the region where vortex F is expected is shown in

Figure 24a. In a moving coordinate system the coherent structure of the jet may

be seen in Figure 24b. The vortex center is located at approximately x = 22.

Then the translational velocity of the vortex between the positions D and F of

Figure 21 is

Ax (22-10) 1/24 ft 24 ft/sec. = 7.3 i/sectime (1/12 sec/cycle) (1/4 cycle)

The instantaneous centerline velocities corresponding to the locations of

vortices D and F are 11.5 m/sec and 10.8 m/sec, respectively. It should be

noted, however, that the vortex translational velocity is only an approximate

value because the determination of the vortex locations is not precise. A

composite view of the streamwise velocity distribution corresponding to the

jet in Figures 24a and b is shown in Figure 15a.

Further evidence of the existance of a large scale vortex structure in the

unsteady jet may be found in the instantaneous decay of the jet centerline

velocity. In the case of steady jets, the centerline velocity decay is a

monotonically decreasing function of streamwise distance. In the unsteady jet

case, the centerline velocity decay (where the centerline is a quasi-sinusoidal

shape) has a typical behavior17 shown in Figure 25. The velocity decays with

streamwise distance, reaches a local minimum and starts to increase again. A

peak is reached, where upon the decay begins anew. The location of the peak

corresponds to the existence of a vortex at that position, as illustrated in

the inset to Figure 25.

Considering the induced velocity distribution due to the vortex and super-

imposing that velocity on a monotonically decaying centerline velocity results

in the typical distribution of Figure 25. Thus the visual observation of a

vortex structure in the unsteady jet is consistent with the quantitative

measurements, specifically the instantaneous velocity structure and its center-

line decay.

5. Discussion

The qualitative similarities between the vortex structure in a forced un-

steady jet and the vortex structure in a quasi-steady jet (at least one that is

15

not driven) suggest the possibility of understanding more of the latter by

studying the vortex dynamics of the former. This may be true not only for

jets but also for the structure of boundary layer flows, particularly those

near transition.

SECTION IV

MULTIJET FLOWFIELD AS A GUST TUNNEL

1. Background

The development of a time dependent flow test facility has been attempted by

a variety of methods. Mitchell 19 employed a technique in which the model was

moved in relation to the flow, passing orthogonally through an open jet wind

tunnel. Gillman and Bennett20 studied gusts produced by a set of airfoils

mounted in a biplane arrangement on the opposite walls of a wind tunnel. As

these airfoils were oscillated in a sinusoidal fashion, they induced an

oscillating flow between them. Other methods include employing moving sinusoidal

waves in the test section walls,21 oscillating the inlet section of an open

circuit tunnel, 22 an oscillating array of airfoils 23 and circulation control

on a set of elliptical airfoils.24

The method which is probably the closest to that of the present investigation

is due to Simmons and Platzer2 s who employed a pair of jet flaps. Each of the

jet flaps is a fluidically oscillating jet driven by a pair of control jets,

one on either side.

2. Operation of the Jets

As a consequence of an effort to develop fluidically controlled time dependent

jets for application to several diverse problems, 3,9 a new technique was proposed

for the construction of a high frequency gust tunnel. 26 A single nozzle was

constructed and tested and is shown schematically in Figure 26.

The method of operation of the nozzle is as follows:

The flow passes through the throat of the jet nozzle (Fig. 26) and into a

rapid expansion region. Because of the relative proximity of the walls, the

flow must attach to one side of the expanded region or the other. This bistable

condition can be strongly influenced by a small pressure difference between the

two sides of the expanded channel. In a normal fluidic oscillator or a fluidically

oscillating jet, 3 this pressure difference is supplied by a feedback system

16

W-7 M.

between the two sides. In the present case, this pressure difference is created

by the rotating valves shown on each side of the jet. The valves are rotated

out of phase with each other, so that one is open when the other is closed.

The resulting flow always attaches to the closed side and thus produces a jet

which oscillates from side to side.

3. Tunnel Concept

The actual gust tunnel design involves a number of these nozzles and is shown

schematically in Figure 27. The tunnel flow passes between the individual nozzles

so that the flow actually guides the tunnel flow from side to side.

Some of the potential advantages of this method of gust generation are as

follows:

1. High frequency capability

2. Low torque motors required

3. Capable of producing transverse or longitudinal gusts

4. Capable of producing various wave forms

5. Capable of producing programmed transverse disturbances

6. Capable of various phase relationships between components

7. Capable of uniform flow across tunnel

It is the purpose of this paper to present the first results of a subscale

multi-jet model of such a gust tunnel and to verify some of the advantages

cited above.

4. Tunnel Geometry

The actual tunnel geometry is shown in Figure 28, along with the details of

the nozzle construction employed here. It may be seen that the scale is

rather small, the nozzles having exit sizes of .508 cm. and being 2.54 cm.

apart. In addition, the depth of the tunnel is only 2.5 cm. The limited

scale leads to some problems because the control valving is not as easily

reduced in size as the remainder of the geometry. There is, for example,

separation of the tunnel flow from the nozzle body just before the nozzle exit,

if the exit velocity is very low.

In spite of the scale problems the nozzles oscillate well and control the

tunnel flow as shown in Figure 29 for the case of all nozzles in phase. The

flow visualization is accomplished by means of kerosine vapor produced by

dripping the kerosine on an inclined resistance heater and entraining the

17

l ~- _____

resulting vapor into the tunnel, between the oscillating nozzles.

The jet exit velocity is 108 m./sec. while the tunnel velocity is 26 m./sec.

The resulting Jet Reynolds Number based on nozzle velocity and exit size is

Re = 3.8 x 104. At an oscillation frequency of 60 Hz, the reduced frequency

is k = .055 based on the nozzle spacing and an average velocity of 40 m/sec.

5. Hot Wire Surveys

A constant temperature hot wire anemometer is employed to survey the

instantaneous velocity field. The particular instrument is a Flow Corporation

(now Datametrics) Model 900 anemometer used in conjunction with a pair of

Thermo Systems, Inc. linearizers. In order to obtain instantaneous velocity

profiles, a triggering system of some sort must be applied to condition the hot

wire signal by deciding when to record the time varying data. In previous jrt

measurements 17 a third hot wire has been employed as the trigger. Although such

a method could also be employed here, there is yet a simpler technique. A

magnetic pickup is used on one of the rotating slot valves so that the posili

of the valve (and hence the position of the corresponding jet) is known as a

function of time. As shown schematically in Figure 30, the triggering signal

from the magnetic pickup is electronically manipulated and used to arm a Schmitt

trigger which in turn controls a sample and hold circuit. Thus the hot wire

continuously samples the flow velocity, but the signals are only recorded when

the flow is in a specified orientation as determined by the rotating valve

position. Then all data recorded with the sampling electronics at a given setting

apply to the same instant in the oscillation cycle and effectively, the data

is instantaneous (as long as the cycles are sufficiently repeatable).

6. Jets in Phase

As discussed in Reference 26, the multi-jet tunnel is conceptually capable

of producing both lateral and longitudinal gusts depending on the phase

relationship between the various nozzles. If the nozzle flows are all oscillated

in phase, they produce a rather large oscillation in transverse velocity (orthogonal

to the mean tunnel direction). This may be seen in Figure 31 and 32.

Figure 31 shows the instantaneous velocity distribution produced by the

nozzles at the instant the nozzle flow is in the extreme upward position. Since

the distance from the nozzle exits is not large (20 nozzle exit sizes), there is

still the evidence of the jet nozzles in the streamwise velocity profiles. However,

even this close to the exits, the velocity ratio between the peaks and valleys has

18

been reduced from more than four at the nozzle exits to less than two. Perhaps

more important is the existance of a strong lateral velocity, equal to more than

3% of the jet exit velocity or almost 10% of the local average streamwise

velocity. The dashed line on the velocity profiles is the zero value before

correction for a bias in the mean tunnel direction.

For comparison, the streamwise and transverse velocities for the case of the

jets in the instantaneous downward position are shown in Figure 32. Thus

Figure 31 and 32 are the same flowfields with a 1800 difference in phase. There

is some shift in the streamwise velocity but an even larger effect may be seen

in the transverse velocity. Thus the difference in the velocity component between

these two particular points in the cycle, is roughly 15-20% of the mean streamwise

velocity.

If the test section is moved to a position farther downstream relative to the

nozzle exits, then the non-uniformity in the streamwise velocity will be

rapidly reduced while the transverse oscillations with time will likewise decrease.

The position of the test section is dictated, to some extent, by the fluid

dynamic problem to be simulated. Farther downstream is probably best for

application to aircraft gust response studies while the conditions reflected

by Figures 31 and 32 are perhaps more appropriate to the study of cascade wakes.

The decay of the jet's velocity and its mixing with the coflowing tunnel stream

is shown in Figure 33 for the case of all jets in phase. Thus by 50 jet widths

downstream, the velocity non-uniformity is only about 7% based on the jet exit

velocity.

An important potential of the present gust tunnel concept is the ability to

create a transverse disturbance which passes across the tunnel. As discussed in

Reference 26, such a disturbance can be generated by designing the rotating control

valves in such a way as to cause the jets to periodically skip an oscillation.

That is, a jet remains attached to one side while the remainder of the jets proceed

through another cycle. This skipping occurs in successive nozzles on successive

cycles, so the disturbance marches across the tunnel test section. This effect

can then be examined as an analogue to rotating stall. However, in order toinclude the required changes in the control valves, the scale of the experiment

must be considerably increased and thus cannot be examined with the existing

apparatus. An alternate method of achieving this effect is discussed below in

relation to a phase lag between the jet oscillations.

19

One difficulty which appears in Figures 31 and 32, and will also be obviousrin the out of phase results, is the end effect of the set of nozzles. These are

a finite number of nozzles in the tunnel and since the nozzle exit velocities are

larger than the tunnel velocity, the tunnel stream is really entrained by the

nozzle flow. Thus the entire set of nozzles entrains the entire tunnel flow,

producing an in flow at the ends of the nozzle bank (i.e., a flow toward the

center of the tunnel). The effect may be seen in the upper portion of Figure 31

when the expected upflow is not seen but is countered by the entrained flow

leading to a very small downward flow. Likewise, in the results of Figure 32, the

expected downflow at the lowest nozzle is countered by an entrained velocity

(producing an upflow) and the result is practically a zero transverse velocity.

It is therefore clear that for application this effect may be minimized by

employing a larger number of nozzles and then making use of the more central

portions of the velocity field.

An alternate point of view is to place the hot wire probe in the flow at a

certain position and then examine the change of velocity at that position as a

function of time (or perhaps more accurately, as a function of phase angle). If

the time varying velocities at various streamwise positions are then plotted on

the same time (or phase angle) scale, the gusts traveling downstream will be clear.

This is the effect seen in Figure 34, where the transverse velocities on the

tunnel centerline at four streamwise positions are plotted as functions of

phase angle. It may be clearly seen that the waves of transverse velocity (or

gusts) travel downstream and that there is the expected phase lag between their

appearance at various positions. The arrows indicate the progression of thesame wave downstream.

7. Jets Out of Phase

In an attempt to produce longitudinal gusts, the relative phases of the four

jets are set such that the two upper jets are 1800 out of phase with the two

lower jets. The two sets of jets are then alternately aimed toward and away from

each other. The flowfield corresponding to these two situations measured at a

position twenty jet thicknesses downstream, are shown in Figures 35 and 36

respectively. It may be seen that in each case the transverse velocity is roughly

zero at the tunnel centerline (after being corrected for the tunnel bias) andconsistant with the jet orientations for positions off the tunnel axis.

20

Especially interesting is the possibility of using the tunnel centerline

position as a test section. Comparing the centerline velocities of Figure 35

and 36, it is clear that a longitudinal gust of roughly 25% of the local velocity

is produced.

The effect of the entrainment of the tunnel flow by the unsteady jets them-

selves is again evident, especially in the upper portion of Figure 36. There

the v velocity component is expected to be positive (upward) but in fact is

somewhat downward (negative) reflecting the presence of the entrainment velocity.

As discussed above, this effect can be minimized by including more nozzles in the

gust tunnel design, or contouring the tunnel walls.

Taking a more detailed look at the centerline velocity change with time, the

results are shown in Figure 37 for various streamise positions from R = 15 to

R = 30. The existance of a wavelike structure at any instant may be seen by

looking at the velocities at the various positions at a particular time. In

addition, the time lag as the wave travels downstream is evident as well as a

distinct change in the shape of the wave. As it moves downstream, the high

velocity portion of the wave expands, probably due to the mixing of the jet

itself.

8. Phase Lag Between the Jets

Consider an alternate phase relationship between the various nozzles as shown

in Figure 38 and 39. There is a phase lag of 450 between each of the nozzle

flow orientations, starting from the top. In Figure 38, the top nozzle is in

the extreme upward orientation, the second nozzle lags it by 450 phase while

the third lags it by 900 phase and is therefore horizontal at the instant shown.

-* The fourth nozzle is instantaneously oriented at 450 phase below the horizontal,

1350 behind the top nozzle. The phase angles do not, of course, correspond

exactly to the physical angles. The arrows on the flow vectors indicate the

direction in which the exit flow orientation is progressing. Thus the top jet

is in the extreme position and stationary while the rest of the jets are moving

toward the top.

The phase positions shown indicate the mechanical position of the control

valves. The actual position of the jets can be somewhat different because there

is some hysteresis in the attachement of the jets. Thus, in the results of Figure

38, the third nozzle is really inclined somewhat more upward resulting in a wider

angle between the flow from the third and fourth nozzles. This appears as a

widening between the velocity peaks formed by these jets, as they move downstream.

21

If the upper nozzle is in the extreme downward orientation and the same 450

phase lag is specified, the velocity profiles are shown in Figure 39. In this

case, it again appears that jet produced by nozzle number three is somewhat ahead

of the phase position indicated by the mechanical positions of the control valves.

Thus the instantaneous orientation of the jet emitted by nozzles 3 and 4 is toward

each other and they produce the double peak shown in Figure 39. This double peakeventually merges into a single peak farther downstream, as was also the case inthe results of Figure 38 where the top two jets merged into a single peak. However,

if there is a phase lag between the jets, even though the upper jets are 1800

out of phase between Figures 38 and 39, the instantaneous flowfields have no such

relationship.

A method was proposed above to produce a disturbance marching transversely

across the wind tunnel. The results in Figures 38 and 39 suggest an alternate

method which will not require more intricate control by means of the rotating

valves on either side of the nozzles. The mechanism is simply to run one of the

jets at a different frequency from the other nozzles which may be in phase with

each other. Thus, the out of phase jet will periodically reinforce one of the

others and this reinforcing will run transversely across the tunnel. It will,

however, run back and forth and therefore requires more adaptation to be useful

for a rotating stall analog.

9. Preliminary Airfoil Tests

In order to have some indication of the interaction of the multi-jet gust

tunnel flow with a body in the test section, preliminary tests are performed with

a simple cambered airfoil at an angle of attach of 180. The jet frequency is 60 Hz

and the flow visualization is again accomplished by vaporizing kerosine. The

results are shown in Figure 40 for every 600 of phase angle.

In Figure 40a, the nozzle flow is in its extreme upward position, although

the phase lag of the flow farther downstream shows a portion of the flow in a

downward motion almost following the shape of the airfoil. With a 600 phase angle,

Figure 40b, the time history of the flow may be clearly seen as it travels down-

stream. The jets are in an orientation which is almost horizontal. Farther

downstream, the prior upward orientation of the jet is evident in the curling of

the streakline over the airfoil. It should be noted here that the smokelines are

streaklines, not streamlines. Thus they do not particle trajectories but rather

the position of a group of particles which have all passed through the same point

at various times.

22

ft,%

The phase lag between the orientation of the jets at the nozzle exits and

the direction of the flow over the airfoil surface appears to be approximately

1800. This may be seen in the cases of 0' and 3600 phase angle (both the same

orientation, of course). In each case the nozzle exit flow is in the extreme

upward position while the flow over the airfoil (and even farther away), is in

the downward orientation.

In these preliminary tests, employing this particular airfoil at 180 angle

of attack, there appears to be no unsteady separation. With the phase lag

discussed above, it might be expected that separation be most likely at a

phase angle of 1800, since the flow over the airfoil will then be in the upward

orientation. No separation is evident at 1800 and in fact the flow is clearly

attached at angles to either side of that value, 1200 and 2400. Further tests

will be required to see if the gust flow can lead to intermittent separation

and thereby a decrease in the mean lift coefficient.

10. Discussion

Subscale experiments with a gust tunnel driven by a bank of unsteady

oscillating nozzles operating in a fixed phase relationship indicate that such

a device can be employed as a means to generate both lateral and longitudinal

gusts. The percentage gust can be rather large, approaching 20% of the meanflow value. For smaller percentage gusts, small spacial deviations in the

streamwise velocity can also be produced. No unsteady separation was found in

preliminary airfoil tests but it is expected that this will occur under some

circumstances.

SECTION V

LINEARIZED UNSTEADY JET ANALYSIS

1. Background

The objective of this section is to propose a method of analysis which may be

applied to the unsteady jet flowfields discussed in the previous section.

Examples of the types of jets which may be treated by the present analysis

are shown in Figures 41-43. The jet exit position of Figure 41 oscillates from

side to side and produces a relatively constant magnitude streamwise wave. In

Figure 42 the velocity vector at the jet exit oscillates in direction and

produces a growing streamwise wave. The unsteadiness of Figure 43 consists of

23

a sinusoidal change with time of the mass flow at the jet exit and thus produces

a nominally constant amplitude wave pattern.

The mathematical complexity of time dependent flows is such that one usually

is forced to resort to one of three possible attacks:

1. A fully numerical solution of the governing equations

2. A phenomenological model

3. The use of limiting assumptions which simplify the governing equations.

A fully numerical solution is possible but requires the dedication of very

significant amounts of time and effort. A recent interesting example of a

phenomenological model is presented by Simmons, Platzer and Smith, 27 who assume

that the unsteady jet may be decomposed into a number of steady jets which

exist during short intervals at the nozzle exit and produce short bursts along

the steady jet trajectories.

Much of the unsteady flow work employing limiting assumptions is based in

principle on the celebrated work of Lin, 28 who analyzed the boundary layer

beneath a time dependent external flow. Lin's technique is limited to high

frequencies and benefits from the fact that the particular problem allows the

specification of an unsteady static pressure distribution within the boundary

layer. The extension of Lin's analysis to the jet case is hampered by the fact

that the time dependent pressure distribution is unknown and there is no comparable

technique to Lin's use of the unsteady Bernoulli equation.

The application of Lin's technique to unsteady jets was carried out by McCormack,

Cochran and Crane 29 for the case of a jet vibrated from side to side at high

frequency (see Figure 41). However, the strict application of the Lin analysis

leads to the conclusion that the convective term in the momentum equation isnegligibly small. This result is not acceptable to McCormack, et al., since itis clear that the convective term is of importance as in the steady flow case.

Thus, McCormack et al. 29 present a phenomenological argument that the convective

term must be included (in spite of the fact that the analysis excludes the term)

and proceed to assume a linear form for it which then results in a linear equation.

The analysis, therefore, is a mixture of types 2 and 3 above.

The present analysis follows the spirit of the linearized jet analyses due

to Pai. 30 The linearization of the equations is achieved by an order of magni-

tude analysis which is rigorous and removes the need for a phenomenological

argument. The requirement of high frequency is also removed and a technique

described for including a time dependent pressure distribution which is produced

by the motion of the jet.

24

2. Relationship Between Steady and Time Averaged Flows

The objective of this study is to determine the effect of the unsteady

flow components on the time averaged flow. That is, what advantages does the

unsteady flow hold in terms of steady state mass and momentum transfer? Theanswer should appear in a steady flow relation including time averaged effects

of the unsteady components.

The two-dimensional boundary layer equations are

45u &u bu I 6p 1 82u

S 6V =0 (2)

where each term is non-dimensionalized so R = Reynolds Number.

Consider the velocity profiles shown in Figure 44. The initial jet velocity

is a function of time while the coflowing stream velocity is steady. Theindependent variables can then be separated into time averaged () and timedependent ( )" quantities with U = coflowing stream velocity.

U(X, y, t)-U+(xy)+u'(x,y,t)

VOX, y, 0) =V(x,y) +v'(x,y, t)

p(x, yt)=5(x,y) +p' (x, y, t) (3)

Substituting the expansions of the independent variables into the momentum

equation and taking the time average of each term results in

60 au [ Bu' 6u'](u+U) + vY I U[' v v yJ Rby2 (4)

It may be seen that the effect of the unsteady terms on the average velocity

is the same as an additional (or artificial) pressure gradient. Thus, if the

time dependent velocities are known, the bracketed term can be evaluated and

the effect of the unsteadiness on the mean flow determined (See Ref. 31).

3. Determination of Time Dependent Velocities

The objective is, therefore, to determine the unsteady velocity components u,

and v', to evaluate the bracketed term in Eqn. 4 and thereby to find the average

velocity distribution U + u, v. Approximate solutions for u and v' can be found

25

- -,.... - .- " .-- - . _

by the following order of magnitude analysis.

Consider the case where the steady state jet velocity deviates only slightly

from the coflowing stream velocity and, as well, the unsteady velocity components

are small compared to the coflowing stream velocity.

Mathematically -

,',v',""<< U (5)

Expanding the momentum equation (1) by the steady and unsteady velocity

components (Eqn. (3) ) results in

6 (U++u') x (U++u') + (U+v') 1y(U+(j+u')

8

(P+p,) + (U+i+u') (6)X R 6y2

In view of the assumptions (5), all products of small variables in Eqn.

(6) are neglected and only terms up to first order in the small variables are

retained.

(Note also that U = constant)

U'+u 40 +U6U'=_p _p+ 1 + U62U (7)6t 6X ax Tx x R V6y2 y2

The steady and unsteady portions of Eqn. (7) may be separated by taking

the time average of (7):

81:1 6P 62iiU _ __ (8).6 x + R 6y2

and subtracting this from (7) to yield

6u' ,u' 6 p' 6 2u, (9)

Et + UTx x + R 6y 2

This, thet., is the governing equation for the unsteady velocity distribution Jfor the jet in Figure 44 with the small perturbation assumptions of equation (5).

The initial condition may be seen from Figure 44 to be a top hat velocity profile

whose magnitude is a function of time. The lateral boundary conditions are that

26

lim u (0)y-W_

The unsteady pressure gradient may, in general, be a function of position

and time,6p" f f(x,y,t) (11

but is not known directly in the jet case. In a later section a technique

is described which allows an approximation to the unsteady pressure distribution.

For the present, the pressure will be neglected and thus the governing equation

reduces to

bu' 6U, 1 U, (12)+ U xx =4 + 6x R (2

This equation is similar to that developed in Reference 29 but in this case

it is not limited to high frequencies and requires no phenomenological arguments.

The initial and boundary conditions are the same as those for Equation (9). The

solution to the linear Equation (12) is

=/ a U ei(wT -wX [erf(1y+ erf(iy](3

whereT = t/R, X x/RU, % v U x=O

and the error function is defined as2f7 e d2 ? (14)

The actual form of the exponential depends upon the initial condition on

the jet. If the initial condition is that the unsteady flow varies about some

mean as a cosine function, then the solution is -

W= cos (wT - wX) erf 1-) + erf 1(15)2 22VY

27 I

4. Determination of the Steady Artificial Pressure Gradient

The overall continuity Eqution (2) can be expanded by the velocity defini-

tions, Eqn. (3), and then split into steady and unsteady forms,

8 8 8b' v,

S0 and + ' =0 (16)

from which it follows that

v o ' 'x dy (17)

Then from Eqn. (15) and (17)

v'= - Ow sin(wT - wx Y[erf 1 - YN+ erf(2._ 1 dy

a cos(wT- wX)fY[exp / )2)' 1 - Y)

+ exp - --- )1+ y\2 11+ y)]8d (18)

28

The resulting artificial pressure gradient term is

= F3 F cos(wT - wX) sin(wT - wX)

+ F1 F4 cos 2(wt - wX)

+ F6 F9 sin(wt - wX) cos(wT - wX)

+ F7 F9 cos 2 (wT - wX) (19)

where the F. terms are independent of time. The averaging of the trigonometric

terms over one cycle results in

cos 2(wT - wX) = /2

sin(wT - wX) cos(wT - wX) = 0 (20)

so-

[ ,x U ,OU'l 2 212

+ - F,F. +-+ F FLY 2

29

L.AI - -

where

F -= H ert -j + erfj 2 V2 2 V'_X 2Yj

___ I [,1Iu\214 = 1 + exp+'+

F= Cr X/, exp [- 3 2k] + exp [ (;: Y4)2]2 V2 T X 2' exp 2

F9 = - U F7 (22)

With the artificial pressure gradient known, the steady state velocity

distribution may be found numerically from Eqn. (4).

It should be noted that the final solution of Eqn. (4) cannot be a

function of magnitude of the jet frequency since none of the terms in Eqn.(22) depend on frequency. The importance of this fact will become apparent in

the next section.

5. Experimental Observations

The jet flow illustrated in Figure 42 has been investigated experimentally,

as shown schematically in Figure 4, to determine the unsteady inputs into the

time averaged jet behavior. The data are taken by a two channel hot wire

anemometer probe, linearized, averaged, and read out on a set of digital volt-

meters. The average is found by an electronic filter designed for this experiment

by McCormick. 32 The jet nozzle is fluidically controlled, as shown in Figure 45,

and is based on a design by Viets.3

A set of time averaged velocity profiles showing the typical development of

the jet in the streamwise direction was shown in Figure 6. The double peaked

profiles are caused by the time dependent flow inclination at the nozzle exit

and disappear as the mixing progresses downstream.

The most important data from the point of view of the present analysis is

shown in Figure 46; the comparison of steady half width growth rates for the

30

. .... II tm'mAd

same jet at various oscillation frequencies. The half width is defined here as the

distance from the jet centerline to the position on the profile where the velocity

is half the maximum velocity found on the profile. It may be seen that there is

an appreciable effect of frequency on the jet half width growth, with the minimumgrowth at a frequency of zero, i.e. the steady two dimensional jet.

If one examines the time averaged term which reflects the effect of un-

steadiness on the mean velocity distribution, Equation (21), it can be seen

that this term is not a function of frequency. This is true since none of its

components [Eqn. (22)] depend on frequency. There are three strong possibilities

for this discrepancy.

a. The analysis is linear while the jet is non-linear.b. The analysis is applicable but the eddy viscosity is not the same as the

steady state (a very likely situation) and is, in particular, a function

of frequency.

c. The time dependent pressure distribution in Equation (9) is not zeroas was assumed earlier in the analysis but is really a function of

frequency.

This possibility is examined in the following section.

6. Effect of a Time Dependent Pressure Variation

The basis for an unsteady pressure distribution is the interaction between

the unsteady jet and the coflowing stream. If one considers the simplest case

of a jet which does not mix with the ambient fluid, then the jet surface appearsas a traveling sinusoidal wave to the coflowing stream. The inclusion of mixing

modifies the shape of this wave but near the jet exit the shape is still very nearly

sinusoidal.

The simplest model for the pressure variation produced by a wave pattern is

that produced by the inviscid flow over a wavy wall, shown in Figure 47. A

linearized treatment of this problem is given by Liepmann and Roshko 33 and results

in the pressure distribution

P a P(- 8 Ea sin ax) (23)

where B depends upon the freestream conditions, P. is the freestream pressure

and the other variables are defined in Figure 47. It may be seen that the pressure

variation is in phase with the wall shape.

The real jet case is, of course, a viscous problem (as is the real wavy wall

31

case). Thus, the pressure dependence is not as straightforward as indicated

above. This has been demonstrated experimentally by Kendall, 34 who studied a

mechanical wave traveling relative to a freestream. Kendall's results indicate

a phase shift between the wall shape and the pressure distribution. The magnitude

of the phase shift depends upon the ratio of the wave speed to the coflowing

stream velocity. For a wave speed approximately equal to the coflowing stream

velocity, the phase shift is approximately 100 downstream.

With the velocity varying as a cosine function as in Eqn. (15), the static

pressure should vary as a sine function. In addition there must be a phase shift

and the boundary conditions require that the pressure approach the limit of the

freestream pressure as the distance from the jet increases. The pressure

dependence satisfying these conditions as well as the requirement that the pressure

be proportional to the square of the velocity difference between the coflowing

stream and wave speed is

Cpp(U - C) e-vfy sin T) - (24)f w(T wX]24

where C may be obtained from Kendall. 34 Including this tem in the governing

differential Equation (9) gives rise to another term in the solution for u

in order to balance the JP term.dxThen

;i . - C , - Cos w(T - TO) - wX (25)L; -0.o U/w

The main point here is that u' now is a function of frequency and therefore the

bracketed term in Eqn. (4) is also a function of frequency. Thus the inclusion

of the time dependent pressure allows the prediction of an average velocity u

which depends upon frequency.

Thus the unsteady flowfield generated by a time dependent jet can be treated

by a linearized attack which is not limited by frequency constraints and evolves

through a rigorous simplification of the equations of motion.

32

SECTION VI

FORCED UNSTEADY FLOW OVER A WING

1. Background

The unsteady jet methods discussed in the previous sections lead to performance

improvements which are due to the increased mixing rate between the jet and the

surroundings. In the present section, a mechanical device will be examined

which drives the flow near a wall to be unsteady. The origin of the present

mechanical system lies in experiments on oscillating airfoil sections. The

airfoil, shown in Figure 48a,is oscillated in a sinusoidal manner about a mean

angle of attack.

As reported by McCroskey, 35 Kramer 36 was the first investigator to discover

that such a dynamic arrangement delayed the onset of stall. That is, the flow

remained attached to the upper surface at higher angles of attack in the

dynamic case than in the static condition. Several investigators have performed

flow visualization studies and found that the oscillating airfoil produces a

vortex structure on the upper surface as shown in Figure 48b. Apparently the

vortices act to energize the boundary layer on the airfoil and thereby delay

separation. A visualization of this flowfield, due to McAllister and Carr 37a

is shown in Figure 49 employing hydrogen bubbles. The sense of the rotation is

in the clockwise direction37b as in Figure 4Bb.

For most applications, the oscillation of the entire airfoil to produce the

desired vortex structure is not really feasible. However, a similar vortex

structure may be generated by a number of simple techniques, one of which is

illustrated in Figure 50. The vortices are created by a cam shaped rotor moving

in the counter-clockwise direction as shown. Each time the rotor surface

discontinuity sweeps by, a vortex is generated in much the same manner as the

recirculation region behind a rearward facing step but with increased strength.

The vortex spacing depends upon the local velocity and the frequency of

generation. The actual geometry of the airfoil used in the present experiments

is shown in Figure 51. A single static pressure tap has been incorporated to allow

a pressure determination of the rotor's utility in the stalled regime.

2. Flow Visualization

The experimental setup, as assembled in the low speed flow visualization

tunnel is shown in Figure 52. The model has a span of 12.7 cm. and since it

33

- .- - "-:'" --- - B Z-.- - ,=-.. -- 'L I' -. T L- - ,i .-

does not span the tunnel, end walls are added to promote the two dimensionality of

the flow. The tunnel itself is a low turbulence open circuit smoke flow visualiza-

tion channel with a 30.48 cm. square test section and a nominal speed of 8 m/sec.

The Reynolds Number, based on the airfoil chord, is approximately 100,000. The

smoke is generated by vaporizing kerosene on an inclined resistance heater and

entraining the vapor into the tunnel inlet.

The flow produced by the rotor mounted in a flat plate is shown in Figure

53. The flow is from left to right and the rotor location is indicated. The

vortex structure may be seen moving downstream until it appears to "burst" in

a fashion reminiscent of transition. This does not mean that the vortex is

destroyed but rather that the external laminar flow becomes turbulent, probably

by entrainment into the vortex structure itself.

On the airfoil, separation first occurs in a limited fashion at an angle of

attack of 140 and the flow is fully separated at 200. This is determined by

observation of the smoke flow structure as well as pressure measurement at the

single static pressure port shown in Figure 51. The pressure measurements will

be discussed in the next section.

The structure of the flow about the airfoil at an angle of attack of 200

and the rotor withdrawn into the body is shown in Figure 54a. In order to avoid

acoustic interaction between the flow and the rotor cavity, the cavity has been

covered by tape. (Although some distinquishable tones were observed at lower

angles of attack, none were found in vicinity of the separation angle). Without

any other changes (except removing the tape) the rotor described above is

activated at a rotational frequency of 2400 rpm and the resulting flow visualization

shown in Figure 54b.

For the sake of clarity, a tracing of the smoke streamline patterns is shown

in Figure 55a. The effect of the active rotor is to draw the streamlines down

closer to the surface of the airfoil and thereby reduce the size of the separated

region. In addition, a streamline which passes below the airfoil in the case of

no rotor activity ( = 0), appears above the airfoil for w = 2400 rpm. This

indicates an increase in the airfoil lift and a reduction in the upper surface

pressure (as will be verified below).

The effect of an intermediate rotor speed is shown in Figure 55b which compares

the streamline pattern for w = 1800 rpm to that for w = 2400 rpm. The intermediate

34

frequency also produces the appearance of an additional streamline above the

airfoil but the deflection of the streamlines toward the upper surface is not

as pronounced as at the higher frequencies.

Thus, based on the flow visualization observations, the active rotor produces

a vortex pattern above the airfoil which energizes the boundary layer and reduces

the size of the recirculation region. The instantaneous flow structure at an

angle of attack of 200 and a rotor frequency of 1000 rpm is shown in Figure 56

and compared to the oscillating airfoil at an instantaneous angle of attack of

210 as shown in Figure 49. The similarity between the two flow structures may

be clearly seen.

3. Quantitative Results

A single static pressure port is built into the airfoil section at the 63%

chord position as shown in Figure 51. Readings are taken at this position

in order to verify the interpretation of the flow visualization results presented

in the preceding section. The variation of the pressure at this point with

rotor speed is shown in Figure 57 for three different angles of attack. The

first, a = 150, corresponds to slight separation. At a = 180 the flow is more

completely separated and by a = 200 the flow is fully separated. While P is the

pressure at the indicated static pressure port, Pfs is the freestream static

pressure upstream of the airfoil location. The difference between the freestream

static pressure and the pressure or the airfoil are presented versus rotor

frequency. The pressure difference is non-dimensionalized with the same pressure

difference at w = 0.From the point of view of performance, the optimum condition is to maximize

the pressure difference since this implies a minimum pressure on the airfoil

(because Pfs is unchanged by the rotor activity). For a = 150, the maximum pressure

difference occurs at 500 rpm and from there the performance decreases. The

reduction is expected since in the limit of very high frequency, the flow cannot

react quickly enough and therefore the problem is again reduced to a steady flow

as far as the fluid is concerned. A similar pressure variation is found at the

intermediate angle of attack, a = 180 At a = 200, the flow is fully separated

and the static pressure port is more deeply submerged in the separated flow. The

maximum pressure difference is now at a higher value of w. The precise location

A cannot be seen due to a speed limit on the present experimental facility. The

35

pressure difference exceeds 35% at a = 200 and implies a similar increase in

lift. However, in the absence of complete pressure distributions along the

airfoil surface, a definitive statement on the change in lift cannot be made.

The variation of the single static pressure with angle of attack of the

airfoil is presented in Figure 58. Again the pressure difference parameter

between the upstream static and the airfoil static pressure is employed, this

time non-dimensionalized with the same difference at w = 0 and a = 0. Considering

first the inactive case (w = 0), the pressure parameter initially rises with

angle of attack (due to a drop in P). A maximum is reached at about 150 where

separation becomes evident. As the separation increases? the pressure parameter

decreases (due to an increase in P) until the flow is fully separated at

approximately 200. A further increase in angle of attack again increase the

pressure parameter. From this point of view, the separation process can be

seen as delaying the rise of this pressure parameter (or slowing the decrease

of P).

If the maximum values of the pressure parameter obtained at a given a

(regardless of the necessary w) are plotted, they lie in roughly a straight

line with the initial pressure rise before separation. Thus the rotor activity

may be viewed as reducing the effect of separation, specifically on the upper

surface pressure and, by implication, on the airfoil lift.

4. Discussion

The purpose of the present section is not simply to propose the vortex rotor

as a method to delay separation, but rather to point out the utility of a time

dependent method of boundary layer control. In this regard, there is no assurance

that the rotor method is superior to, say, an oscillating plate 3sa ,b which alternately

protrudes from and withdraws into the surface of the airfoil. The choice of the

rotor was due to the obvious vibration advantages of a rotary motion over the

reciprocating motion. This is especially true if the rotor is designed so that

it is dynamically balanced. There are certainly other time dependent devices

which are capable of producing the same vortex structures, such as an oscillating

air brake configuration.

No attempt has been made to optimize the performance of the rotor in terms of

position on the airfoil or size relative to the boundary layer thickness. The

boundary layer in the present experiment is thinner than the protrusion of the

36

rotor. However, in other experiments related to the vortex generation upstream

of a ramp, (see following section) the boundary layer was substantially thicker

than the protrusion of the rotor and the boundary layer was turbulent. Neither

of these conditions had any detectable negative influence on the ability of the

rotor to generate vortices.

As noted in the description of the experiment, to obtain the base case of

no rotor, the rotor is withdrawn into the airfoil and the cavity covered with

tape. The purpose is to avoid an acoustic interaction with the cavity flow

which could have a strong effect on the flow over the airfoil. Such a tunable

cavity which improves the ability of the flow to remain attached has been proposed

by Quinn. 39 The acoustic disturbance produced by the cavity appears to energize

the boundary layer. The acoustical effect has been observed in the present

experiment with untaped cavities at lower angles of attack. Since the present

cavity is not tunable (except in the sense of a change the static position of

the rotor), it would not be expected that the acoustic effect would be everywhere

evident.

Both the acoustic effect and the present mechanical method are examples of

employing unsteady flow in an advantageous manner. The acoustical method is

attractive because of its relative simplicity since it only requires an

adjustable cavity. The mechanical method reduces the complexity of the cavity

but requires the additional input of energy into the rotor. It does, however.

have the potential advantage of allowing a variable input of energy into the

boundary layer control.

Thus the use of time dependent lateral vortices to energize the boundary layer

appears to warrant further investigation in terms of more quantitative results and

optimization of the configuration.

SECTION VII

UNSTEADY FLOW OVER A REARWARD FACING RAMP

1. Background

The control of boundary layers in an adverse pressure gradient is of interest

in a variety of applications where separation is to be avoided. This is, of

course, especially true for transportation systems where the desire to reduce

drag is driven by economic and speed objectives. In addition, aircraft need to

37

avoid separation in order to maintain the required lift force.

Boundary layer control has historically emphasized three methods; blowing,

suction and vortex generation. The blowing method adds energy in the lower

boundary layer and suction removes the low energy flow from the same region.

The vortex generation method neither adds nor removes mass but rather causes an

interchange of mass between the outer flow and the lower boundary layer. Thus

the flow near the wall is energized and able to overcome a larger pressure

gradient. The vortices are of two types, longitudinal (or streamwise) vortices

which are continuously created at a streamwise position and lateral (or cross

stream) vortices which are formed by some non-uniformity in the surface and

swept downstream. The strength of the lateral vortices is limited by the

velocity of the freestream flow while the frequency of generation is limited

by rate at which the vortices are shed by the generator. The vortices thus

created deform into three dimensional shapes as they are swept downstream.

In order to achieve an independent control over the strength and spacing

of the lateral vortices, the present paper considers their generation by an

active device and their effect on a flow geometry conmnon to transportation

systems, the rearward facing wedge or boat tail. For internal fluid dynamics,

the shape also corresponds to a half diffuser and many of the results herein

presented will refer to that device.

2. Vortex Generator

As discussed in the introduction, the field of fluid dynamics has generally

avoided unsteady flows wherever possible because the unsteadiness has often

been associated with undesirable consequences such as noise and material fatigue.

In some cases, however, unsteady flows are unavoidable (for example in turbo-

machinery) and in others desirable results are produced by the unsteadiness (forexample the unsteady jet results of Sections II - V.

The time dependent vortex structure considered in this section is produced by

the cam shaped rotor shown in Figure 59a. The flow is from left to right and

the rotor turns in the counter-clockwise direction. The discontinuity in the

rotor surface generates one lateral vortex for each turn of the rotor. The

effect of the vortices is to energize the lower portion of the boundary layer

and enable the flow to withstand stronger pressure gradients. T;,e mechanism

by which this is accomplished is probably the actual exchange of low energy

fluid in the boundary layer for higher energy fluid from the mainstream. It

38

should be emphasized that the direction of rotation of the cam is such that it

does not push the flow. Thus the energy put into the rotor is only the small

amount required for the mass exchange, not the energy put into the boundary

layer (which comes from the freestream).

Figure 59b shows the particular geometry of interest here, a half boat tail

geometry (which could also be considered a half diffuser from the point of view

of internal flows). Such a method is a potential way of filling the wake of

a bluff body to reduce the drag. More generally, the technique is representative

of a positive view of unsteady flow which searches for beneficial aspects of

unsteady flows as opposed to those leading to performance degradation.

The structure of the vortex field downstream of the rotor is shown in

Figure 53 for the flat plate case (e = 0). The flow is made visible by the

addition of smoke upstream. The location of the rotor is labeled and the

approximate locations of the vortex centers are indicated by the bulges in the

streamlines nearer to the wall. The vortices are swept downstream so that their

spacing depends directly upon the flow velocity and inversely upon the rotor

speed.

The experiments are performed in a low speed smoke tunnel. The remainder

of the tunnel is constricted so that all the flow is forced through the

duct and over the rearward facing ramp. The velocity produced upstream of the

ramp is nominally 32 m/sec resulting in a Reynolds number of 1.97 x 106 per

meter. The distance the rotor extends into the flow is .381 cm. and the Reynolds

number of the rotor, based on its height and tip speed at a rotational speed of

1000 rpm is 256. The boundary layer thickness at the rotor location is

approximately .635 cm. and is turbulent due to the rough inlet extension of the

plate and a trip upstream. The remainder of the flow through the device is low

turbulence level, having passed through a dozen upstream screens. A smoke

generator was employed to produce visible streamlines to be entrained into the

tunnel inlet. In the case of unsteady flow these lines are, of course, streak-

lines (as seen in Figure 53) rather than streamlines and their interpretation is

less straightforward.

3. Quantitative Results

Two methods are employed to assess the utility of the vortex generator

described above. One is to visualize the flow by the use of smoke and will be

treated next. The other is to measure the pressure distribution along the ramp

39

M .

and the velocity just upstream of the rotor. When the flow is attached to the

ramp, the pressure distribution resembles that through a diffuser; a low

pressure rising to a level higher than the upstream value. In the present

experiment, the downstream pressure is relatively fixed (neglecting any fan

stall) so that changes in the flow are reflected as changes in upstream static

pressure.

The pressure distribution corresponding to a ramp angle of 200 is shown in

Figure 60. The pressure levels are referred to the ambient static pressure

values upstream of the ramp Pf. The pressures are obtained by a Statham

pressure transducer which is calibrated by means of a Merriam micromanometer.

Pressure taps are located at various positions on the ramp and the freestream

pressure and velocity are obtained by means of a pitot-static tube. The

difference between the ramp pressure, P, and the upstream pressure, Pfs. is

non-dimensionalized with the dynamic pressure and plotted versus the streamwise

distance normalized with the upstream wall sepearation (Figure lb.). It is

clear from Figure 60 that the ramp flow is attached even without the rotor

operational since the pressure rises along the ramp to a value above the

freestream value. It should be noted that the no rotor (w = 0) cases are

obtained with the rotor cavity covered with tape to avoid any acoustic effects.

fhe use of the rotor at a speed of 2500 rpm has no major effect on the flow. The

rotor does appear to slightly improve the flow attachment along the ramp as

evidenced by the reduced pressure distribution. Farther downstream the pressures

for the two cases are indistinguishable.

The situation changes considerably when the ramp angle is increased to 28' as

shown in Figure, 61. For the case of w = 0 (i.e. rotor unused), the pressure

distribution on the ramp deviates only slightly from the freestream value. This

indicates the flow is separated at the ramp and therefore the effective area

that the flow experiences is nearly a constant area duct. The use of the rotor

at 1000 rpm reduces the pressure distribution at the beginning of tie ramp,

indicating that the flow more easily negotiates the turn.

As the rotor speed increases above 1000 rpm, the static pressure on the ramp

decreases, indicating improved flow performance. The performance at rotor speed

of 4000 and 5000 rpm is virtually indistinguishable, suggesting that this speed

range may contain the maximum performance in terms of w for this particular case.

That question cannot be completely answered here since 5000 rpm is the upper range

40

--- .

of the present experimental capabilities.

As the ramp angle is increased to 30° (Figure 62), the separated flow (for

= 0) reacts even less to the presence of the ramp; the pressure distributiondeviates even less from the freestream value. The general behavior of the

flowfield with increasing w is similar to that at 280. As the rotor speed is

increased, the pressure distribution on the ramp decreases. Again, the difference

between the 4000 and 5000 rpm values is very small.

The main difference between the performance at 280 and 30' is in the actual

level of the pressure changes. The pressure rise along the ramp at 280 is

twice that at 300. Thus it is clear that the flow at 300 is more difficult to

control than that at 28', although in each case the use of the rotor improves

performance. This is not unexpected especially when one considers the additional

energy involved in turning the flow an additional two degrees. The performance

may perhaps be improved at 300 if more energy is put into the rotor, most likely

by simply increasing its size. The present facility is not capable of such a

change.

4. Flow Visualization Results

The smoke flow photograph in Figure 53 as well as those to be presented here-

after, are obtained by the entrainment of kerosine smoke into the tunnel inlet.

ihe smoke is produced by allowing liquid kerosine to drip slowly on an inclined

plate heated by a resistance element. As the kerosine flows down the plate, it is

vaporized. A fan blows over the plate and drives the kerosine vapor to the tunnel

inlet where it is released at several points and entrained into the tunnel.

The photograph in Figure 53 was obtained by a single strobe flash and, therefore,

is a relatively instantaneous view of the flowfield. Several longer time exposures

(1/100 sec) of the flow over the ramp are shown in Figure 63. The wall angle is

280 and the rotor speed varies between w = 0 in Figure 6a to w = 4000 in Figure

63d. As the rotor speed increases, the positions of the mean streamlines move

closer and closer to the ramp, indicating better flow attachment and verifying

the pressure measurements of Figure 61.

Perhaps of even more interest are the high speed photographs of Figure 64 a-f

for various rotor speeds at a ramp angle of 280. For a zero rotor speed and the

cavity taped, the flow clearly separates as shown in Figure 64a. There is some

large scale structure in the separated shear layer but not enough momentum transfer

to lead to reattachment. If the rotor is activated with w 1000 rpm (Figure 64b),

41

the separated flow curves down toward the ramp surface, very much in the same

manner as the time averaged picture at the same rotor speed, Figure 63b.

With a rotor speed of 2500 rpm (Figure 64c), the curvature of the flow

toward the ramp becomes more pronounced. In addition, the time dependent

structure becomes significantly larger. A vortex may be seen in Figure 64c,

with a region farther downstream which appears to be separated. The sequence

of events appears to be as follows: Suppose the flow is initially separated.

The rotor generates a vortex which causes the flow to attach for a moment before

it is forced to detach again by the adverse pressure gradient. At this time

the flow needs a new vortex to force it to attach again. If the speed (or

effectively, the generation frequency) is sufficiently high, the necessary

vortex is available.

The flow situation described above may be seen in Figures 64d and 64e for

both of which w = 4000 rpm. The two photographs indicate considerably different

flow patterns. Actually they are examples of the same time dependent flow at

two different times. These are the extreme positions of the oscillatory flow

pattern at 4000 rpm. The mean pressure distribution on the ramp reflects

the time average of the oscillatory flow. The instantaneous flow patterns,

Figures 64d, e are fully consistent with the time average flow pattern of

Figure 63d, where the apparent lack of smoke near the wall is due to the fact

that the streakline is there only intermittently. It should be noted that

the position of the incoming smoke is unchanged in the sets of photographs

resulting in Figures 63 and 64.

The transition between the flow patterns of Figures 64d and e is shown in

Figure 64f (for a speed of 5000 rpm). The flow far down the ramp is clearly

separated while that nearer to the corner is relatively attached. The attache,;

flow is produced by the vortex sweeping downstream, momentarily overcoming the

adverse pressure gradient, as discussed above.

5. Three Dimensional Rotor

The foregoing results employ a rotor which is uniform in cross section

throughout its length. Of course, in terms of application the rotor must end at

some point. In addition, there are some applications where a uniform rotor must

be integrated transverse to an axisymmetric geometry (i.e. perpendicular to a

round pipe). Thus the question of a three dimensional rotor is of interest.

42

The three dimensional rotor geometry employed here is shown in Figure 65. On

the centerline of the rearward facing ramp geometry, the rotor cross section has

the same shape as the uniform rotor employed in the earlier parts of this section

and shown in Figure 59. However, as one moves away from the centerline (i.e. into

or out of Figure 59) the size of the rotor tapers to zero at a transverse position

of 3.6 cm from the centerline. Another difference is that there is no undercut

in the rotor shape but the discontinuity in the rotor shape is merely a straight

step. The subsequent flow visualization results and pressure measurements are

all made on the centerline of the flowfield.

The effect of the magnitude and direction of the rotation speed on the ability

of the flow to remain attached to a 280 ramp is shown in Figures 66 and 67. The

detached flow for the case of no rotor is shown in Figure 63a. The flow separates

imediately at the beginning of the ramp. The nominal velocity at the top of the

ramp is 32 m/sec. The photographs in Figures 66 and 67 are taken with a

sufficiently long time exposure so that the results are essentially a time average

of the flowfield and hence are average streamlines.

In Figure 66 the comparison is made between rotation in the counter-clockwise

(+) direction and the clockwise (-) direction for speed of 1000 and 2500 rpm. The

direction of rotation does not appear to be a major effect, but the rotation has

not yet caused the flow to turn the corner very effectively. With an increase of

rotational speed to 4000 and 5000 rpm, the effect of the rotation direction

becomes very pronounced. In particular, at w = ±5000 rpm the effect is very

strong, resulting in a fully attached flow for a counter-clockwise rotation and

a fully separated flow for a clockwise rotation.

The time average pressure distribution on the ramp are shown in Figures 68 and

69 for two sets of rotational speeds, ±1000 rpm (Figure 68 and ±5000 rpm (Figure 69).

At the lower rotational speeds, the pressure rise on the ramp is rather small and

only weakly affected by the direction of rotation. This is consistent with the

results of Figure 66 and indicates that the frequency of vortex generation is

too low to achieve sufficient boundary layer energization to allow the flow to remain

attached. Changing the direction of rotation (at the same w) keeps the frequency

of vortex generation unchanged but changes the strength of each vortex because the

relative velocity between the stream and the rotor Is changed. However, since the

frequency of generation is insufficient for attachment even with the counter-

clockwise rotation, the effect is minimal.

43-rI

At higher rotational speed, however, the effect of rotational direction is

very significant as shown in Figure 69 for the case of ±5000 rpm. The counter-

clockwise rotation (+) produces the stronger vortex and leads to a higher pressure

rise on the ramp. This result is a reflection of the improved flow attachment

on the ramp and verifies the flow visualization results of Figure 67.

The details of the flow structure may be seen in the streakllne photographs of

Figures 70 and 71. In this case, the photographs are taken with a single

flash strobe and thus yield the instantaneous positions of the entrained smoke or

streakline. The interpretation of streakline patterns is more difficult but

can be guided by observations of their dynamic behavior as observed with a

tunable strobe light. The results at the lower rotational speeds, Figure 70,

verify the results of Figure 66 in that the effect of rotation direction is

not very strong and indeed, the ability of the unsteady energization to cause the

flow to remain attached is rather limited. However, at larger rotational speeds,

Figure 71, the effect of rotor direction is very pronounced, leading to a very

strong vortex structure and a successful attachment when rotated in the counter-

clockwise (+) direction. When rotated in the clockwise (-) direction, the

strength of the vortices produced is greatly reduced (since the relative velocity

is reduced) and the resulting flow is not well attached to the ramp.

Thus the time dependent method of boundary layer energization appears to show

promise from the point of view of application. Rotation in the upstream direction

(+) direction is desirable to maximize the relative velocity between the rotor

and freestream and thus maximize the vortex strength. Three dimensional rotors

show the same promise but additional data is needed on geometrical effects.

6. Discussion

The results presented above indicate the usefulness of unsteady flow to control

boundary layers in the face of adverse pressure gradients. In this case the

unsteady structure is created by a rotating cam but the present design of the

cam (or indeed the use of a cam itself)is not intended to suggest an optium

configuration. Rather, the objective of this section is merely to point out

the potential advantage of unsteady flows.

The unsteady structure can also be accomplished by various other devices such

as oscillating spoilers, plates or even membranes. The advantage of the rotor

system is primarily that the reciprocating motion has been avoided. In addition,

with the use of modern composites, the rotor could be built as designed and yet be

well balanced, again avoiding troublesome vibrations.

44

SECTION VIII

INDUCED UNSTEADY FLOW IN A DUMP COMBUSTOR GEOMETRY

1. BackgroundIThe dump combustor, illustrated schematically in Figure 72 (from Drewry40 )involves a rapid diffusion of a duct flow by the geometrically simple device

of a step enlargement in the duct diameter. The recirculation region thus

produced acts as a flameholder and keeps the flame from being blown downstream

by the high speed flow. Therefore, the reciruculation region is designed to

act as an ignition for the main flow passing through the duct. In order for

ignition to be accomplished, there must be an interaction between the two

flow regions. It is the purpose of this section to propose a simple mechanical

method which indicates a potential performance improvement since it increases

the fluid dynamic interaction between the recirculation region and the main

flow.

The method proposed here is demonstrated in a two-dimensional arrangement

although most dump combustor applications for ramjets are axisymmetric. This

is due to the relative simplicity of the 2-0 device but the same principle can

be applied to the axisymmetric case, probably in the form of segmented rotors

or several rotors around the periphery of the duct.

Dump combustor performance, especially as it relates to ramjets, has been

studied by several investigators40-43 both analytically and experimentally. The

present experiment is performed at relatively low speed and aimed at a flow

visualization understanding of the process, verified by time averaged pressure

measurements.

The objective of an increased flow interaction which leads to improved

performance is not unique. One of the more successful attempts has been by

Choudhury44 who introduced jets from the walls immediately upstream of the dump

station. In some cases these entered at some oblique angle to the wall and

thereby produced a swirling inlet flow which improved the performance of the

combustor. The jets, unfortunately, require relatively high pressure gas which

must be carried with the flight vehicle and included in an assessment of the

overall performance. The use of swirl to increase combustion efficiency has

also been investigated from the point of view of heating furnaces45 and the

mixing of jets.46

~45

2. Experimental Apparatus

The two-dimensional half dump combustor geometry employed in the present

experiment is shown in Figure 73a. Three step sizes are considered, h = 1/3,

2/3, 1. The nominal upstream velocity is 120 ft/sec with some variation with

overall performance. As in the schematic of Figure 72, the flow separates at

the corner and forms a recirculation region. In order to increase the inter-

action with the main fiow, the device illustrated in Figure 73b is proposed.

It consists of a simple cam shaped rotor which turns in the counter-clockwise

direction and produces a transverse clockwise vortex with each sweep of the

rotor's surface "discontinuity". A rotor of this type can be shown to be a

useful tool to energize the boundary layer and to reduce problems associated

with separation on airfoils (Section VI) and diffusers (Section IX). It

should be emphasized that these effects were obtained with rotation in the

counter-clockwise direction so the rotor simply does not push the flow downstream.

In the present case the objective is not only to energize the boundary

layer but to actually cause a time dependent variation in the structure of

the recirculation region. That this is accomplished may be seen in the flow

visualization results of the following section. The rotor method employed

here is not expected to be the only way to generate such an unsteady flow

structure. A similar effect could be obtained by the use of an oscillating

plate which appears normal i the surface in a sinusoidal fashion. Another

possibility is the use of an oscillating air brake (a plate in the surface

hinged on the upstream side and alternately raised and lowered from the surface).

3. Flow Visualization Results

The flow is rendered visible by the entrainment of smoke into the inlet of

the open circuit wind tunnel. The smoke is generated by vaporizing drops of

kerosine on an inclined resistance heater. The resulting time averaged

streamlines are shown in Figure 74a for the case of no rotor motion (i.e., the

rotor withdrawn into the surface and the cavity covered). The time averaging

takes place over the exposure time, 1/100 sec. The length of the recirculation

region is approximately eight or nine step heights as compared to a length of

eight step heights in a comparable high speed axisymmetric experiment.40 That

the activation of the rotor decreases the average length of the recirculation

region may be seen in Figure 74b where the rotor speed is 1000 rpm. The reduced

46

:- .. ..' . . . ' I ;: " .. .' ' l ... . .. .. = 7 ~

length is approximately 7-8 step heights. Increasing the rotational speed

produces yet a further reduction in the average recirculation zone length, as

seen in Figure 74 c-e. Although, it is not possible to determine the length

with any precision, it is clear that increasing the rotor speed decreases the

average length of the recirculation zone. The difficulty in resolution is

caused by the fact that the flow is not steady and thus the photograph, even

using a short time exposure, is smeared due to the rapid changes in structure.

In order to show the instantaneous structure of the flow, a single flash

strobe light is employed. Even with moderate camera speed, the strobe captures

the time dependent motion as may be seen in Figure 75, showing the streaklines

for the case of no rotor activity (w = 0). The breakdown of the shear layer

into a larger scale structure may be seen near the end of the separated region.

The length of this recirculation region is approximately 8-9 step heights as

was estimated from the time averaged photograph, Figure 74a.

The introduction of unsteady flow by means of the rotor results in very

significant time dependent changes in the flow structure. Some indication of

this effect is seen in Figure 74 b-e where the spreading of the streamlines

indicate their extreme positions. More dramatic evidence is presented in the

following set of figures for the case of w = 2500 rpm. Figure 76a shows the

structure of the flow as not much different from that of zero rotor speed,

Figure 75. However, at another instant of time, Figure 76b, the structure is

quite different. The tail of the recirculation region has been swept away while

*the upstream portion is relatively unchanged. At yet another instant, Figure

76c, the recirculation region has again attained the expected elliptical shape

*but with a much decreased length. The interaction of the two flow regions is

very strong with the length of the recirculation (or flame holding) region

effectively pulsing back and forth. In the combustion case this should lead

*to improved performance.At higher frequencies, the vortices generated by the rotor are closer

*together and their influence on the flowfield can be even stronger. An instantan-eous streakline for a rotor speed of w = 5000 rpm is shown in Figure 77. In

terms of its relation to the cyclical behavior of the recirculation region,

Figure 77 is probably comparable to Figure 76b. That is, the longer recirculation

region of a prior time is being shortened by the vortex structure and the end of

47

the region Is shed. The interaction may be seen to be very strong indeed. The

upsweep of the streamline at the dump position Is typical of the higher rpmvalues of the rotor (for this step), while at lower rpm's the flow separates

practically parallel to the upstream surface.For the largest step size considered in this experiment, h - 1, the available

distance downstream is not sufficient for reattachment to take place. However,

the change in character of the time average streamlines with changing rotor

speed, is still evident in Figure 78. In the case of an inactive rotor (w a 0),

the streamlines separate at the corner and become smeared farther downstream due

to the very turbulent structure developed in the shear layer. When the rotoris activated, the size of the recirculation region is reduced with increasing

rotor speed. At w = 5000 rpm, its length is estimated to be four step heights.The instantaneous streakline structure of the flow over the h 1 step is

shown in Figure 79. For w = 0, the streakline shows little distinctive

structure and is similar to the upstream portion of that for the smaller stepheight and w = 0, Figure 75. However, the use of the rotor produces, as in

the smaller step case, a very strong vortex structure, appearing in Figure 79b

at only one step height downstream. There results a clear and strong inter-action between the recirculation region and the main flow. A similar structure

is evident at higher rotational speed, w = 5000 rpm, in Figure 79c. There

is no indication in the large step case of the separation at an angle to the

upstream surface as observed in Figure 77.

From the preceeding Figures, especially Figures 76, 77 and 79, the potential

advantages to a dump combustor due to the introduction of a time dependent

vortex structure may be seen in a qualitative fashion. A quantitative lookat the time averaged pressure distribution and the effect of the rotor ispresented in the following section.

4. Pressure Distribution

The streamwise pressure distribution is obtained from static pressure orifices

mounted in the wall downstream of the dump corner. A Statham pressure transducer

is employed along with a Daytronic Model 601B signal conditioner and a Datametrics

digital readout. The simple pressure transducer is used to obtain all readings

and is calibrated before and after each run with a Meriam Micromanometer. The

static and total pressures upstream are obtained in order to determine the upstream

velocity and a base for the pressure distributions.

48

The static pressure downstream of the corner for a step height h = 1/3 is

presented in Figure 80. The basic effect of unsteadiness on the time average

flow is seen to be the shortening of the recirculation region length. That is,

the pressure reaches its maximum at a streamwise distance which is inversely

proportioned to rotor speed. The maximum pressure position is not the re-

attachment point since it has been shown,40 based on flow visualization, that

reattachment occurs upstream of where the maximum pressure is attained. Thus

the reattachment, in the case of the withdrawn rotor (w = 0) should occur before

ten step heights (where the maximum pressure is attained). This is consistant

with the estimate of eight or nine step heights from Figure 74a. For a high

rotational speed of 5000 rpm, the average reattachment point should occur

before the maximum pressure is attained at x = 6. This, to, is consistent

with an estimate of four to five step heights based on the flow visualization

in Figure 74e.

With a change in step height to h = 2/3, the results in Figure 81 are produced.

At this step height, there is insufficient streamwise distance available in the

present experimental setup to allow for reattachment, at least for the zero

rotation case. However, the question of performance is clear since the use of

the rotor allows a more rapid and substantial pressure increase. Here the

rearward facing step acts more like a diffuser. That is, if the step is to act

as a diffuser, then the flow should at least partially reattach to the lower

wall. The more complete reattachment yields a more rapid pressure rise. The use

*of the rotor aids reattachment and thus results in a larger pressure rise.

The same situation is true for the case of = 1, Figure 82 where length

of the lower plate is only on the order of three step heights. Here, too, the

use of the rotor allows the rearward facing step to act as a better diffuser.

The flow, however, retains its unsteady nature and thus its major advantage from

*the point of view of interaction of the main flow and the recirculation region.

The decision to drive the rotor in a counter-clockwise direction is motivated

by three objectives. One was the aim, in an earlier experiment involving an

airfoil (Section VI), to produce an unsteady vortex pattern similar to that

found above an airfoil with a time varying angle of attack. The second objective

is the overall one of this entire sequence of experiments; to demonstrate the

advantageous use of unsteady flow. In that regard, rotating in the counter-clockwise

direction clearly relies on unsteady flow to energize the boundary layer since the

upper surface of the rotor is moving upstream, and therefore cannot simply push

the boundary layer flow downstream.

49

The third objective is to produce strong and concentrated vortices. To

achieve this effect, it is desirable to maximize the relative velocity between

the flow and the rotor. This is, of course, attained when the flow and rotor

tip are moving in opposite directions.The effect of the direction of rotation is examined in Figure 83 for h 1.

The positive direction is that involved in the previous results, counter-clockwise

rotation. For rotational speeds of 1000 and 2500 rpm (both positive and negative),there appears to be little dependence of the streamwise pressure distribution

on sign. However, for w = ±4000, the difference is significant, amounting to

roughly a 10% improvement in static pressure rise for the counter-clockwise

rotation. For the reasons mentioned above, this improvement was anticipated. The

surprise is that the same effect did not appear at lower rpm values. Theresolution between anticipation and results is shown in Table 1.

As the rotor turns, the streamwise component of its tip speed, both

maximum and average, are calculated as compared to the nominal freestream

velocity of 123.5 ft/sec. It may be seen that for a rotor speed of 2500 rpm,the maximum streamwise velocity of the tip is moving at a velocity less than

7% difference from the flow velocity. The average velocity difference is even

smaller, being slightly over four percent.Thus the change in vortex strength with rotor speed is not very high and

does not have a significant effect until w = 4000 rpm where the maximum change

exceeds 10%.

Although the effect of direction is not very important until higher rotational

speeds, it may be seen (from Figure 80-82) that the effect of speed is still

very significant. Therefore the primary effect is not one of vortex strengthbut rather vortex spacing (or frequency of generation). The flow, then, requires

the passage of a vortex with a minimum frequency in order to retain the favorable

aspects of the unsteady flow.

One final point to be examined is to ensure that the rotor is not simply

acting as a trip which could be replaced by a static one. A comparison is pre-

sented in Figure 84 between a dump flow without any rotor and one in which therotor is in a fixed upward position, acting as a static trip. The rotor in such

a position is even out performed by the no rotor case which leads to a higherdownstream pressure and thus acts as a more effective diffuser in the steady sense.

50

5. Discussion

The use of time dependent flow to enhance the interaction between the flame

holding recirculation region in a dump combustor geometry and the main flow

appear to have very significant potential for performance improvement. The

device proposed here is certainly not the only manner in which this potential

can be realized. Numerous other techniques could be devised to employ the

advantages of time dependent fluid mechanics. Further work is needed to determine

the quantitative effect on a combusting system.

SECTION IX

PERFORMANCE POTENTIAL OF UNSTEADY DIFFUSERS

1. Background

Artificially induced large scale flow structures have been employed

successfully in the past to improve performance. Two examples are the common

streamwise vortex generators sometimes used to control the flow over an aircraft

wing and to maintain attached flow in large angle diffusers. In each case,

streamwise vorticeF are created which cause a transfer of energy from the outer

flow to the boundary layer. The large scale streamwise structures are

created by the passive vortex generators simply mounted in the surfaces.

Transverse flow structures have also been examined as a method to control

boundary layer separation. Quinn 39 employed a transverse cavity to generate anacoustic disturbance in order to keep the flow over an airfoil attached at

high angles of attack. Stull et. al. 47 used spacers to build transverse

, cavities on diffuser walls. Standing vortices were produced in the cavities

in an attempt to improve the diffuser performance. A transverse standing

vortex, driven by a control jet at a fixed position in the diffuser was

examined by Haight and O'Donnel.48 The device, named the trapped vortex

diffuser, led to a performance improvement.

The objective of this investigation is to examine the potential performance

advantages of a diffuser in which the flow is forced to be unsteady. There are,

of course, various methods which can be employed to force the flow, including

adapting Quinn's acoustic method, 39 mechanically controlled boundary layer

injection4 and boundary layer blowing controlled by fluidic means.3

51

The question of the response of a diffuser flow to an unsteady input has

been examined experimentally by Stenning and Schachenmann4 9 and analytically

by Schachenmann and Rockwell. 50 Their investigations had a different perspective

because they recognized that diffusers often need to operate with an unsteady

inlet flow and that the effect of this time dependency on the overall performance

is of significant interest. In the present case, the time ;candency is forced

in an attempt to improve the performance of the device.

2. The Forced Diffuser

The method considered here is a simple mechanical device illustrated in

Figure 85. A spiral shaped rotor is mounted in the wall on each side of the

channel just upstream of the diffuser section. The rotor surface has a

discontinuity which ends in a cusp. The rotor turns in such a direction that

the motion of the portion exposed to the flow is always against the flow, i.e.

the upper rotor turns in a clockwise direction while the lower rotor turns in

the counter-clockwise sense.

Each time the surface discontinuity of the rotor is swept through the fluid,

a vortex is formed which then is convected downstream. The rotors (and hence

the vortices) can have an arbitrary phase relationship. In Figure la the rotors

appear simultaneously and thus the vortices are formed in phase with each other

and are symmetrically positioned. Figure lb illustrates the out of phase

condition where the discontinuities appear alternately and thus the vortices

formed are staggered as they sweep downstream.

The experimental geometry shown in Figure 85 has the following scale:

D = 15.2 cm; L = 30.4 cm: h = .38 cm; and the nominal inlet velocity is V = 40

m/sec. The resulting range for the nondimensionalized angular velocity of the

rotors is approximately 10 < < 20 where Z = wD/V.

The rotor device in Figure 85 has been successfully applied in other flow

situations, in particular on an aircraft wing (Section VI) and just upstream of

a rearward facing ramp (Section VII). The ramp problem approximates a half

diffuser and is therefor of particular interest here. In the ramp case it was

shown that for sufficiently large angles (roughly above 250) the flow separates

at the corner rather than turning through that angle. The addition of the

rotating vortex generator in such a flowfield, allows the flow to turn through a

larger angle.

52

Thus the use of the rotors is designed to allow the diffuser to operate at

a larger area ratio without separation. The unsteady vortex structure energizes

the boundary layer and allows it to overcome a larger pressure gradient. The

vortex structure produced by the rotor is shown in Figure 86 by means of kerosine

vapor streaklines. The vortex, at the instant of the photograph, is located

somewhat downstream of the diffuser corner.

As the rotor speed increases with a fixed tunnel speed, the spacing of the

consecutive vortices decreases, as well as the size of the vortices themselves.

This effect may be seen in Figure 87 where the streamwise velocity through the

diffuser has been held artificially low in order to more clearly illustrate the

structure. The lowest photograph is at a rotor speed of w = 1000 rpm with an

increase of 1000 rpm to each photograph above. Thus the number of vortices

seen in the photographs is proportional to the rotor speed.

The beginning of flow separation in the diffuser (without a rotor) may be

seen in the e = 800 and 120 cases in Figure 88, showing both flow visualization

and exit velocity profiles. The separation may be clearly seen in the exit

profiles, to occur at the lower wall, resulting in a profile which is skewed

toward the upper wall. The velocity coordinate is nondimensionalized with the

inlet velocity and the distance with the inlet dimension D. It should be noted

that the exit size is larger in the 120 case than the 80 case so the separation

is even more substantial than is apparent at first glance. The profiles are

taken with a hot wire anemometer employing a low pass filter to produce the

time average readings. The photographs are taken with a single flash strobe and

thus show the streakline pattern.

A comparison of the flow patterns with and without the use of a rotor is shown

in the photographs of Figure 89. In this case the exposure time of the film

is much longer and the result is an effective time average resulting in a

streamline pattern. In each case the diffuser angle is 2e = 300. The upper

case employs no rotor and strong separation is apparent from the lower wall of

the diffuser. The lower photograph employs a rotor at a nondimensional speed

of = 11.84 with the rotors in phase with each other. The separated region

has moved to the upper wall and has been significantly reduced in size.

3. Performance

The performance of the various diffuser combinations are compared by means of

the nondimensional pressure rise (or pressure recovery) through the device. The

53

L.53

S* _-- -- y . - --- -

7 M M-- -. --

nondimensional pressure, P is defined as the difference between the wall pressure

within the diffuser and the inlet pressure, divided by the inlet dynamic pressure,

P =wall -P inlet

1PV2

The pressure rise with nondimensional streamwise distance is shown in

Figures 90-92 for the case of an out of phase orientation of the two rotors.

The pressure rise is plotted for various rotor speeds including the case of

W = 0 which corresponds to no rotor and having the rotor cavities covered to

avoid acoustic interactions. The lowest angle case is shown in Figure 90,

2e = 16. As was evident in Figure 88, there is no separation within the

diffuser at this angular setting. This is also verified by the similarity in

the pressure distributions on the opposite sides of the diffuser for W = 0

in Figure 90. Since no separation exists, the use of rotors cannot improve

the performance and, in fact, results in a performance reduction.

Increasing the diffuser angle to 2e = 240 results in a separated flow, as

previously seen in Figure 88 and verified by the pressure distribtuions of

Figure 91 for w = 0. In this case, the use of the rotors results in roughly

the same performance although there is a positive trend with rotor speed. In

addition, with the use of the rotor, the pressure distribution on both

walls assumes the shape corresponding to attached flow. At the highest angular

setting, 2e = 300, the overall performance decreases. However, the use of

the out of phase rotors results in a significant performance improvement

compared to the no rotor condition.

The corresponding results for the in-phase orientation of two rotors are

shown in Figures 93 and 94. For an angular setting of 2e = 240, the pressure

rise on the two walls of Figure 93 indicate a small performance improvement

due to the use of the rotors. Perhaps even more important is the positive

trend with rotor speed that is evident. For the largest diffuser angle tested

2e = 300, the in-phase rotor results (Figure 94) indicate a very substantial

performance improvement on both walls.

4. Flow Structure

Instantaneous velocity profiles are taken within the diffuser by employing

a hot wire anemometer along with a conditioned sampling device. The hot wire

54

produces a continuous signal. The conditioned sampling circuit only accepts

the hot wire signal when the rotor is instantaneously in a predetermined

position. A probe traverse under these conditions results in the instantaneous

velocity profile which exists each time the rotor is in that particular position.

The input required to define the rotor position comes from a magnetic pickup

on the rotor drive shaft. A more detailed description of the data aquisition

system is given in the following section. The magnetic pickup can also be used

to trigger a strobe light and thereby produce streakline photographs of the

diffuser flowfield with the rotors in a particular predetermined phase position.

A combination of the instantaneous flow streakline pattern produced by flow

visualization and the corresponding instantaneous velocity profiles can be

an aid to the identification of the large scale flow structures and are shown

in Figures 95 and 96. The in-phase configuration for an angle of 20 = 241 is

shown in Figure 95. It is evident that the basic flow is attached to the upper

wall and that the forced unsteadiness modifies that condition. The flow

visualization reveals a strong vortex near the lower wall at o = 1800. Since

the rotors are in-phase there is a corresponding mirror image vortex near the

upper wall which does not appear to be as large and also is located further

downstream. Both of these effects are consistent with the flowfield since the

growth of the vortex is inhibited by the proximity of the wall and the vortex

is convected more rapidly due to the higher velocity near the fully attached

wall. The presence of the vortex at the 1800 phase angle is verified by the

superimposed streamwise velocity profile which is enhanced near the center of

the channel and reduced in the region between the vortex and the wall. Both

effects are caused by the induced velocity due to the presence of the vortex

pair.

With the rotors in the in-phase orientation, the flowfield is expected to

have a pulsating character due to the time dependent change of the blockage

at the diffuser inlet. This effect is evident in the flow visualization result

at * = 900 where the pulsing appears to be almost symmetrical. The effect may

also be seen by comparing the instantaneous velocity profile at 0 = 900 to that

at o = 1800. The former profile is wide and relatively uniform while the latter

is constricted at the edges and accelerated near the center.

Streakllnes with superimposed velocity profiles are shown in Figure 96 for

an out of phase rotor orientation and a larger diffuser angle 20 = 30° . In this

55

case the basic flow is attached to the lower wall of the diffuser. The

instantaneous phase angles of the individual rotors are indicated on each side

of the diffuser. Due to the out of phase orientation of the rotors, the flowfield

has essentially a flapping character. This is most evident in Figure 96d. The

vortices appear to be located in the vicinity of the measuring station in (b) and

d). In each case, the upper vortex in (b) and the lower vortex in (d), the

presence of the vortex results in a decreased velocity near the wall and an

increased value near the centerline. These velocity changes may again be

attributed to the induced velocity of the vortex structure.

In order to more clearly specify the effect of a vortex on the flowfield

(and thus be more capable of identifying the vortex location) consider the

schematics of Figure 97. The objective is to demonstrate the local change

in velocity, both streamwise (u') and transverse (v'), produced by the presence

of the vortices which are shown schematically as swirling fluid near each wall.

The vortex near the upper wall is rotating in the counter clockwise direction

while the vortex near the lower wall rotates in the clockwise direction. The

qualitative transverse velocity changes, u', (equivalent to the induced velocity)

may be seen not to depend upon whether the profile is taken in front or in back

of the vortex location but does depend upon the sense of rotation of the vortex.

Thus the streamwise velocity profiles can be used to determine the sign of the

vorticity.

The qualitative effect on the transverse velocity change (v') indicates that

there is a sign change from the upstream to the downstream side of the vortex

and also a sign change with the sign of the rotation itself. However, it is

not possible to distinquish between, for example, the upstream side of a counter

clockwise vortex from the downstream side of a clockwise vortex. Thus both

velocity profiles are required, but knowing both can result in the identification

of the vortex.

In order to verify the schematics of Figure 97, consider some data taken from

the in-phase results of Figure 95. In particular, compare the velocity profiles

for the case where a vortex pair is present (0 = 1800) near the measuring plane

to a case where no vortices are present (0 = 900). This comparison is presented

in Figure 98. The difference in the streamwise velocity corresponds, for both

the upper and lower vortex, to the situation of the profile being taken on the

downstream side of the vortex as in Figure 97. This is certainly consistant with

56 J........

the flow visualization results at * = 1800 of Figure 95. Comparison of the

transverse velocity profiles verifies this conclusion since the difference

qualitatively agrees with the schematic profiles downstream of the vortices

in Figure 97.

Consider now the case of the out of phase results of Figure 96. A vortex is

evident near the upper wall of Figure 96b while none appears near that wall in

Figure 96d. A comparison of the streamwise and transverse velocity profiles

of these cases is shown in Figure 99. From the streamwtse comparison, it is

clear that the vortex is turning in the counter clockwise direction when

compared to Figure 97. The difference between transverse velocity profiles

indicates that the profile containing the vortex (Figure 96b, * = 900) wastaken upstream of the vortex. This result may be seen to be consistant with

the streakline photograph of Figure 96b.

Thus the forced time dependent diffuser flows appear to have potential to

improve the performance of the device. In the present case, the time dependency

has been mechanically created. Of course, other possibilities exist which may

have advantages in terms of construction, reliability or cost.

SECTION X

DETAILS OF THE FLOW PRODUCED BY THE ROTOR VORTEX GENERATOR

1. Background

The existence of large scale, unsteady structures in flows which are nominally

steady has been noted by Roshko and others. 11 These structures are currently

under intense investigation due to their relationship to the turbulence

structure and eventually to computational analysis, perhaps employing an eddy

viscosity. The coherent structures seem to have a strong effect on the transport

properties of flow systems. Their effect is yet amplified by the fact that

they survive and remain coherent for very large characteristic flow times.51

Of course, large scale flow structures have often been employed to enhance

the momentum transfer between various flow regions. The common vortex generators

found on aircraft wings produced streamwise vorticity in order to energize the

boundary layer and thereby avoid separation. Large scale streamwise vorticity

57 .

has also been employed to enhance the mixing of a jet with the surrounding fluid.5 2 ,5 3

Perhaps more effective but certainly more difficult to produce is the generation

of transverse vortices in the jet, lying parallel to the plane of the jet exit.

Such structures have been produced by acoustical bombardment,' mechanical

interference2 and fluidic switching 3,9 and significantly improve the mixing rates.

The purpose of the present section is to examine the generation of transverse

vortices near a wall and their effect on the overall flow. The mechanical

vortex generator is shown in Figure 100 and consists of a simple cam shaped rotor.

The flow is from left to right as shown and the rotor turns in the counter-

clockwise sense. Each time the rotor surface discontinuity is exposed to the flow,

a vortex is generated in a manner similar to the generation of a starting vortex

by a rapidly accelerated airfoil section. The vortex then is swept downstream

by the flow and causes the transfer of momentum in the vicinity of the wall.

2. Potential Applications

As discussed in the preceeding sections, the vortex generator shown in

Figure 100 has been tested in several flow geometries. Included are the case

of a vortex generator on an airfoil to delay separation and stall (as shown

schematically in Figure 50), vortex generation to allow the flow to turn a

larger angle (as shown in Figure 59) and the use of vortex generation in a

combustor to potentially improve the flowfield (as shown in Figure 73).

In both the airfoil and ramp applications, the advantage of the rotor

technique is primarily the improvement of the time averaged flow, even though

the flow must be unsteady to produce this benefit. In the case of the rearwardfacing step (Figure 73), the primary benefit is the actual time dependency

produced by the rotor. The objective is to increase the interaction between

the recirculation region behind the step and the remainder of the flowfield. The

rotor causes the recirculation region length to pulsate and has potential

application to the improvement of dump combustors.

3. Flow Visualization Results

The rotor shape shown in Figure 100 was originally a simple spiral in which

the rotor surface gradually transitioned from a smaller radius to a larger oneand then abruptly returned to the smaller radius. Then the step from the larger

to smaller radius was undercut in order to produce a cusp at the rotor tip and

thus improve the vortex generation process.

58

The flow structure produced by the spinning cam shaped rotor may be clearly

seen by employing smoke flow visualization. The smoke is generated by dripping

kerosine on an inclined resistance heater. The vaporized kerosine is released

through tubes located at the tunnel inlet and entrained into the test section.

The following photographs are obtained by the use of a strobe light so they

indicate the instantaneous position of the smokelines. Since the flow is

unsteady, these lines are not streamlines but rather streaklines. Their

interpretation is less straightforeward since their position represents the

integrated effect of everything upstream. However, in this case the interpre-

tation is considerably simplified by the fact that the flow can be observed

dynamically. This is achieved by allowing a small frequency difference between

the rotor and the strobe light, which effectively produces a slow motion version

of the flowfield. The significance attributed to the following figures is

guided by this dynamic view of the flow.

The tunnel itself is an open circuit low velocity, low turbulence tunnel with

a dozen inlet screens to break up the large scale motions in the entrained air.

The velocity in the test section is uniform within 4% without the rotor activated.

The boundary layer thickness is less than .64 cm. (.25 inch). The velocity at

the rotor position is 11.6 m/sec (38.1 ft/sec) and the rotor extends a distance

of 2.54 cm (1 inch) into the flow in its fully extended position as shown in

Figure 100. The resulting Reynolds Number is 1.98 x l04, based on the rotor size

and freestream velocity. Of course, the Reynolds Number will change with relative

velocity between the rotor tip and the freestream.

Six rotor speeds were examined by the flow visualization technique in order

to examine the effect of generation frequency and vortex strength. The signifi-

cant parameters are listed in Table 2.

Typical of the desired vortex generation is the result shown in Figure 101

for a rotor speed of 3000 rpm. The strobe lighted photographs have been arranged

in the order of their occurrence, from top to bottom. As the rotor tip sweeps

from right to left, the first hint of the vortex produced is seen in the lowest

smokeline which begins to curl up in Figure lOla. By Figure lOlb the rotor tip

has disappeared and the vortex is evident, slightly farther downstream. The

streaklines still appear to be relatively laminar but in Figure lOlc the vortex

flow appears to be turbulent with a smaller scale structure visibly. By Figure

lOld the size of the vortex structure has grown considerably and it has translated

59

downstream as well as rising, higher above the surface of the plate. Its position

yet farther downstream is shown in Figures lOla, b and c where its continued

growth and interaction with the outer streaklines is evident. In summary, the

vortex is produced by the rotor shape, grows and transitions to a turbulent

state and is convected downstream. Its energization of the boundary layer flow

can be inferred from the results cited in the preceding sections.

The tip of the rotor is moving in the upstream direction in the previous case

and a strong vortex is apparent. Turning the rotor in the opposite direction

at the same speed (i.e. - 3000 rpm) generates vortices at the same frequency

and rotating in the same sense. This indicates that the relative velocity between

the rotor and freestream is still in the same sense. For this case the relative

velocity in Table 2 is in the opposite sense, indicating that the local stream-

wise velocity is slightly increased by the presence of the rotor. In general,

for rotation in the clockwise direction the strength of the vortex is greatly

reduced by the lowered relative velocity. Such a case is shown in Figure 102

for various rotor positions. The vortex is clearly formed, stays near the wall

and eventually bursts into turbulence. The interaction with the stream is

minor due to the weakness of the vortex.

Decreasing the rotor speed to +2000 rpm in Figure 103, produces a somewhat

weaker vortex than the +3000 rpm case of Figure 101. The rolling up of the flow

is very pronounced but the disturbance is not as strong. Turning the rotor in

the clockwise sense so that the tip moves in the same direction as the free-

stream velocity, results in a stronger vortex in this case (Figure 104, W = -2000

rpm) than that produced in Figure 102 (w = -3000 rpm). This is simply due to the

fact that the relative velocity is increased between the rotor and the freestream.

Further results, Figures 105 and 106, compare the case of rotation at ± 1000 rpm.

Again, the frequency of vortex generation is the same with rotation in either

sense, but for this speed the vortices are rather weak in either case. Neither

disturbance is very large and the curling up of the streakline is not very evident.

The magnitude of the disturbance appears to be roughly the same in either case.

Thus the flow visualization results clearly show the existence of a vortex

structure downstream of the spinning rotor. The frequency of generation depends

upon the rotational frequency since each rotation produces one vortex. The

strength of the vortex depends upon the relative velocity between the motion of

the cusp tip and the freestream velocity.

60

. .

4. Quantitative ResultsThe flow geometry described above is examined quantitatively by employing

a hot wire anemometer. A Flow Corporation (Now Datametrics) Model 900 constanttemperature anemometer is employed in conjunction with a pair of Thermo SystemsInc. linearizers. Since the instantaneous velocity field is required to study

the vortices and their effect, the hot wire signal must be conditioned so that

the only velocity recorded is at a predetermined phase angle of the rotor'smotion. The technique is to mount a magnetic pickup on the shaft of the rotor,

so that the position of the rotor is known. As shown schematically in Figure 107,the triggering signal from the magnetic pickup is electronically manipulated and

used to arm a Schmitt trigger which in turn controls a sample and hold circuit.

The hot wire continuously samples the flow velocity, but the signals are onlyrecorded when the rotor is in a particular orientation. Thus, all data recorded

with the sampling electronics at a given setting apply to the same position of

the rotor and the data is instantaneous (as long as the cycles are sufficiently

repeatable).Combining the streamwise, u, and transverse, v, velocities, the entire flow-

field can be depicted by plotting the magnitude of the total velocity and its

orientation as the length and angle of vector arrows in a field. Such a field isshown in Figure 108, where the rotor is in the 0 = 00 (i.e. the maximum extension)position. The velocity vectors shown are the instantaneous values at that

particular phase position of the rotor.

Examining Figure 108, there is no evidence of the existence of a vortex inthe flowfield. However, in order to see the coherent motion of a portion of

matter, the observer should be in a frame of reference moving with its centerof mass (as discussed in Section III). In the field of Figure 108, this can beaccomplished by simply subtracting the velocity of the center of the particular

vortex. Of course, the location of the vortex center is unknown, so the processinvolves some trial and error. However, the flow structure which leads to a

vortex can be isolated. It consists of a curved instantaneous streamline in thevicinity of which the magnitudes of the velocity vectors simultaneously increase

with distance from the center of curvature of the streamline.By the above method the approximate location of the vortex center may be

located. In Figure 108a, for example, the instantaneous streamlines are highly

curved and appear to satisfy the necessary form at a streamwise location X = 7.5.

61

Choosing an intermediate streamwise velocity from this profile and subtracting

it from all the velocities in the field reveals the structure of the vortex,

Figure 108b. Its center is located at approximately X 7.5, Y 3.5. No

other vortex is apparent.

One third of a cycle later, the rotor is instantaneously positioned at an

angle e = 1200 as shown in Figure 109a. At this time, the vortex located at

= 7.5 for e = 00 must be located farther downstreai.. The anticipated structure

is found and the transformed structure (obtained by subtracting a velocity 11.8

m/sec) is shown in Figure 109b, clearly illustrating a vortex centered at

10.5, Y = 4.75.

Searching the field of Figure 109a, it appears that another vortex may be

present very close to the rotor position itself. The velocity profiles are taken

as continuous profiles, so additional detail is shown in Figure 109c. Identifying

the typical structure and subtracting a velocity ot 130.0 m/sec results in

Figure 109d where the vortex is evident at a location X 1.5, Y = 1.25. That

this vortex was not observed in the e = 00 case indicates that it was not yet

large enough to be identified.

One third of a cycle later, the rotor is in the e = 2400 position. The

flowfield corresponding to this time is shown in Figure l1a. Searching for the

typical structure described above, it is apparent that two vortex structures are

present. Subtracting streamline velocities of 13.0 m/sec and 11.0 m/sec reveals

vortices at locations X = 4.5, Y 2.0 and X = 13, Y = 5.75 as shown in Figures

110b and c respectively.

Of course, the various vortex structures illustrated above are really the

same vortex observed at different times as it is swept downstream. The variouspositions and phase angles are plotted in Figure 13 and show the trajectory ofthe vortex to be an almost linear rise after its structure is established. Based

on the trajectory, the translational velocity of the vortex is approximately

constant and equal to the undisturbed freestream velocity, 11.6 m/sec (38.1 ft/sec).

The average translational velocity, based on the positions and phase angle shown,

is 10.7 m/sec.

The trajectory of the vortex, as shown in Figure 111, also explains why the

vortex generator is so effective even if it is submerged within a boundary layer

as in Section VII. The vortex is created with a very small core which grows

rapidly and it rises out of the boundary layer. Thus the scale of its influence

becomes larger as it moves downstream and it moves into a better position from

62

which to energize the boundary layer.

The influence of the vortex on the streamwise velocity is shown in Figure 112.

The strearnwise velocity profiles are plotted along with the position of the

instantaneous vortex. The vortex clearly produces an overshoot in the velocity

profile; that is, a velocity higher than anywhere else in the field. This over-

shoot must be the result of the vortex since the rotor is turning in the wrong

direction to generate such a streamwise increase. In addition, the vortex flow

produces a flow to the wall which energizes the boundary layer.

Analytically, Theisen54 has examined the character of boundary layers and

wakes with discrete vortex structures. In agreement with experimental

observations, he derived a separation criterion which is related to the flow

intermittency and burst frequencies. Such a method could be especially useful

in the optimization of a vortex generator from the point of view of frequency,

once the optimum shape has been found. Walker and Abbott55 have analyzed the

case of a vortex moving near a wall. Unfortunately, their vortex rotates in

the opposite sense. Nevertheless, the implications of some of their results

parallel those above.

The identification of the vortex structures in the present case is rather

straight-forward since the forced time dependent flow is so strong. If the

unsteadiness is weaker compared to the mean flow, the structure may be more

difficult to distinquish. A method to handle this situation has been developed

employing a discrete Fourier Transform and will be discussed in the next section.

The locations of the individual vortices may then be deduced from the angles

produced in the transformed plane.

Another interesting aspect of the velocity profiles of Figure 112 is the

apparent potential for viscous drag reduction. The existence of the vortex

in the field lowers the velocity near the wall below that which would normally

exist. In this way the velocity gradient at the wall is reduced, as is the

instantaneous viscous drag. The effect of this reduction on the mean viscous

drag is currently being investigated. The entire situation is reminiscent of

the use of a vortex sheet to produce the required boundary condition in

potential flow.

5. Discussion

The results presented above show the generation and subsequent dynamics of

the unsteady vortices produced by a mechanical rotor operating near a wall.

63

The very large scale vorticity and structure shown here has two main applications.

One is to explain the success achieved with vortex generators in various appli-

cations. The second is to use these readily identifiable structures in order to

test methods of determining large scale vortex structures in nominally "steady"

boundary layers. Success in identifying the large scale steady structures would

then allow the modeling of a real steady turbulent boundary layer with both its

large scale structure and small scale viscous structure.

SECTION XI

DATA ANALYSIS TO IDENTIFY LARGE SCALE VORTEX STRUCTURES

1. Background

The recent interest11 in large scale coherent flow structure is due, to a

large extent, to the inadequacy of present analytical and empirical methods of

treating turbulent flow. The large scale structure leads to an increased

mixing rate and is thus of great importance in systems which are mixing limited.

However, the presence of the structure is difficult to determine in a quantita-

tive fashion. Qualitative results in nominally steady flow have been presented by

Brown and Roshko 14 among others. An example of a large scale structure in an

unsteady jet is shown in Figure 3, employing smoke flow. The quantitative diffi-

culties are, to a large extent, due to the fact that the large scale structures

are convected with the local fluid velocity. Therefore, in order to correctly

identify the structure, one needs to know the approximate convection velocity.

Of course errors in the assumed convection velocity would also change the

appearance of the large scale structure. Therefore, it is desirable to develop

a method of identification of the large scale motions and thus determine their

convection velocities.

The present method applies a discrete Fourier transformation to a general

velocity field on a point by point basis. The resulting transformed field

yields a distinctive signature of the passing large scale structure. Then

knowing the locations of the large scale structure, the convection of these

points can be determined.

The eventual aim of this approach is to identify the existance of large

scale structures in places where one might not easily find them, such as in

transition from laminar to turbulent boundary layer flow. Their existence in

such places would yield valuable information on the transition process itself.

64

Coherent structure is also expected in fully turbulent jets and boundary layers.

The question of how to define a vortex in more complicated flowfields has

been treated by Lugt,56 who points out that there exist situations in which a

flow may have instantaneous streamlines which form a closed loop and yet the

actual flow does not swirl (i.e. the path lines are not closed). The question

may be especially difficult in the case of time dependent flows. In the

unsteady situation, Lugt's definition of a vortex requires that it be possible

to find an inertial frame in which the streamlines are closed and the centers

of the closed regions do not move. This is a much stronger definition than

simply closed streamlines. It implies that the vortex pattern must be convec-

ted at a constant velocity. Perhaps the definition should be extended

slightly to simply state that, in order to ensure that a vortex exists, one

needs to find instantaneous closed streamlines and to show that this pattern

is convected with the mass of which it is composed, regardless of how the

translational velocity changes with time.

2. The Transformation Technique

The discrete Fourier transformation maps a complex matrix of size N by

N2 into another complex matrix of the same size by the equation:

N1-l1N2-1 -J (Tr km + L" en)

F (m,n) f (k,)e ()

k=O e=O

where f(k,k) is the discrete function in the original plane at points k,t and

F (m,n) is the corresponding spectrum.

2a. A Single Vortex on Axis

The original two dimensional spatial plane, which contains complex velocity

components as a function of position, is mapped into a two dimensional frequency

domain as shown in Figure 113. The velocity distribution in the physical plane

is shown in Figure 113a. By the transformation Equation (1), the resulting

transformed plane is shown schematically in Figure 113b. At each matrix

* location, the transformed plane is complex, the horizontal direction being real

while the vertical direction is imaginary. Thus each entry in the matrix consists

of the magnitude and phase angle of the spectral components.

65

--- . ' a 'z __ ; ,' , - . IL . ,_ 2 ..... - r, . ' , -- 1 . - ,i i ..

For this particular case of the vortex existing on the axis of the physical

plane, the complex entries in the first matrix row are all real and have

phase angles 0 = . The entries in the first matrix column are all purely

imaginary and have phase angles € = -w/2. In the present case the vortex

is rotating in the counter-clockwise direction. If the vortex rotation is

reversed to the clockwise direction, the directions of the entries in the

first row and first column are also reversed, resulting in phase angles of

S= 7r in the first row and 0 = n/2 in the first column. The actual phase

angles are shown in Table 3.

2b. A Single Shifted Vortex

Now consider the case where the vortex is not located at the axis of the

real plane but rather at some arbitrary location shown in Figure 114a. The

vortex is shifted by Q units out of a total of N2 matrix points in the horizontal

direction and by P units out of a total of N1 matrix points on the vertical

axis. The effect of this shift of the vortex center upon the transformed matrix

is shown in the schematic of Figure 114b. The phase angle of any point in the

matrix is shifted from its original value (for the vortex at the axes) to a

new value which is proportional to the product of the vortex shift distance

and the particular matrix location.

So for any point in the first row of the matrix

*(on) = o(o, n) -2 n Q (2)

where n is the matrix column number, Q is the shift distance from Figure 114a and00 is the phase angle in the unshifted case. Thus, by examining the difference

between the phase angles of the shifted and unshifted vortices, the shift distance

Q may be identified. Likewise, the phase angle change for the matrix points in

the first column is

¢(m,o) = 0o (m,o) -- 2wmP (3)

where m is the matrix row number, P is the shift distance from Figure 114a and

€0 is the phase angle in the unshifted case. At a general transformed point

* (m,n) = *o(m,n) - mP - n-

66

However, for the purpose of identifying the vortex location, the axis values are

the simplest to handle.

The actual spectrum phase angles for the shifted vortex case are shown in

Table 4. The shift of the vortex may be computed from Equations (3) & (4) to be

P = 50 and Q = 64 (out of an 89 x 89 matrix) and may be verified by the shift

shown in Figure 114a.

2c. A Constant Magnitude Rotation

The two previous examples have dealt with a classical vortex velocity

distribution with a solid body rctation near the center (i.e. velocity proportional

to radius) and velocity inversely proportional to radius farther out from the

center. In order to ensure that the particular velocity distribution in the

rotational flow does not affect the technique proposed to locate the center of

the motion, consider the case shown in Figure 115. The magnitude of the

velocity is constant throughout the plane and the center of the motion is on

axes. The phase angles in the most important portion of the frequency plane

are shown in Table 5 and confirm the result that the spectrum is real in the

first row and imaginary in the first column.

2d. A Convected Vortex

Consider now the case of a vortex which is not at rest relative to the coordinate

system but rather is convected with the flow at some translational velocity.

The velocity, as shown -in Figure 116a, is then more complicated at least in the

sense that the vortex center may not be clearly seen. As discussed earlier, the

vortex may be seen in a coordinate frame noving with the velocity of the vortex

center itself. Of course, in order to find that frame, the vortex center must

be found. Since the present field is a generated example, the translational

velocity field is known and its transformed matrix may be examined separately.

The variation of translational velocity is shown in Figure 116b while the

superimposed vortex is that in Figure 114a.

The transformed matrix of the entire flowfield of Figure 116a is shown in

Table 6, while the transformed matrix of only the translational component,

Figure 116b, is shown in Table 7. The translational component only produces

a change in the first column of the matrix while the rest is zero. Thus the

inclusion of the translational flow variation only contaminates the first column

of the entire transformed flow as shown in Table 6. This may also be seen by

67

comparing Table 6 with Table 4, the transformed vortex alone.

Thus the location of the vortex being convected in this parabolic translational

flow can be found by applying Equation (4) to any other matrix points except

those in the first column. In general, the original angle in the unshifted

case o would not be known since it would depend to some extent on the velocity

distribution in the vortex. The Q shift could be found by applying Equation

(4) to the first row where o is known to be zero. Then knowing Q, the P

shift may be found by applying Equation (4) to the diagonal elements of the

matrix where it is known that the 0o values are all equal.

The vortex location is identified by the above method and the translational

velocity at that point determined. Subtracting the local velocity at the center

of the vortex from every point in the velocity field transforms the observer

into a coordinate frame moving with the vortex. The result of this computation is

shown in Figure 116c.

If the velocity in the N, direction varies only with the N2 direction and

simultaneously the velocity in the N2 direction varies only with the N, direction,

then the effect on the transformed frequency plane is only to contaminate the data

in the first row in addition to the contamination of the first column. In this

case it will be necessary to again make use of the fact that the diagonal of

the transformed unshifted vortex has equal elements in the angle matrix. Since

the phase shift is linear, Equation (4) can be applied to two sets of points

on the diagonal to generate two equations for the two unknowns, P and Q.

3a. Identifying A Single Vortex In A Real Flow

The instantaneous flowfield structure of an oscillating jet has been determined

in Sections II & III and found to contain large scale unsteady vortices which

are convected downstream. A time slice of this flowfield is shown in Figure 117 and

corresponds to the instant that the jet is in the horizontal position and

sweeping from top to bottom. No vortex is apparent in Figure 117 for the same

reason none could be seen in Figure 116a. Transforming the velocities of Figure

117 by Equation (1) results in the partial matrix shown in Table 117. Applying

Equation (4) and the techniques of the preceeding section results in identifying

the vortex center shifted P = 8.34, Q = 2.15 from the upper left corner point.

The total velocity at that point is found and subtracted from every point in the

physical plane, Figure 117, and results in the structure shown in Figure 118. Here

68

the coordinate frame is moving with the velocity of the point identified as the

vortex center and indeed a vortex is apparent, centered at the identified point.

3b. Identification Of Multiple Vortices

In general, there is no reason to limit the search for vortices in a flowfield

to a single vortex. Depending upon the size of the region and the type of fluid

flow problem, there may be a number of vortices present. The technique shown

below to determine the location of two vortex centers in the field may be

extrapolated to as many more as necessary.

The two-vortex velocity field is shown in Figure 119. Not only are there

two vortices in the field but the fields of the individual vortices strongly

overlap one another. The transformation of this velocity field by the discrete

Fourier Transformation, Equation (1), results in the partial matrix of phase

angles and magnitudes shown in Table 9.

The flowfield containing two vortex centers, as shown schematically in

Figure 120a, can be transformed into a single matrix. This one matrix can in

turn be degenerated into two component matrices, each of which represents one

of the component vortices as shown in the schematic Figures 120b and 120c.

Choosing four matrix points in each of the transformed planes, an equation of

the form of Equation (1) can be written for each of the points. Then the eight

points in Figures 120b and 120c result in eight equations and 12 unknowns Q1,

Q2, P1, P2 , anm, amn, anon,, an'm., bmn, bnm, bnim,, bmin . However the magnitudes

of the spectrum are symmetric about the diagonal so am = anm, bnm = bmn etc.

Then the system is reduced to eight equations with eight unknowns and solved to

yield the vortex locations Pl, Qi and P2 , Q2-

Numerically, the solution is accomplished in the following manner. A guess

is made for the vortex locations, P1, Qi and P2, Q2. With these four variables

defined the system is reduced to eight equations and four unknowns. This will

then yield two solutions for each of the four unknowns. The guess of the vortex

locations resulting in the smallest difference between these two solutions is

the correct location of the vortices.

Such a search has been accomplished for the double vortex generated velocity

field shown in Figure 119 and resulted in vortex locations of 64,50 and 60,39 in

the 89 by 89 matrix which are the exact positions of the computer generated vortices.

Thus the technique works well for a set of well defined vortices.

69

4. Multiple Vortices In Real Flows

The same technique is applied to a real flow containing multiple vortices by

examining the flow shown schematically in Figure 100. A cam shaped rotor is

turned in the counter-clockwise direction in a freestream flow from left to right.

Each time the surface discontinuity is exposed, a clockwise vortex is generated

and is convected downstream as shown in the smoke photograph of Figure 101. This

flowfield has been discussed in Section X. An example of the instantaneous

velocity field is shown in Figure 121, based on conditionally sampled hot wire

anemometry data. In Section X, this data was shown to contain two convected

vortices as may be seen in Figure 109 at a different instant of time.

Analyzing the velocity field of Figure 121 by the multiple vortex technique

described in part 2f results in the identification of two vortex centers located

at positions 13,4 and 7,22. By a visual technique of examining the wave pattern

produced by the convected vortices in the velocity field, the location of the

vortex centers have been estimated at 10,3 and 3,19. Thus the multiple vortex

transformation analysis produces reasonable accuracy in spite of the fact that it

only employs four data points in the vortex field. This is even more remarkable

when one considers that the real vortices are imperfect due to the accuracy limita-

tions of the measurements and the existence of other constituents in the field.

The accuracy of the technique could be improved by employing more data points

or perhaps a regression analysis. However, one objective of the present effort

is to develop a technique which can be applied to fields where the data is sparse.

In addition, the numerics are purposely held to a minimum in order to allow the

examination of large flow areas.

Having determined estimates of the vortex locations as described above, the

velocity fields in the coordinate frames moving with those vortices are found

by subtracting the translational velocities at the centers from each velocity

vector in the field. The results are shown in Figure 122a for the upstream

vortex and in Figure 122b for for the downstream vortex. The presence of the

vortex structure is clear in each case and having thus been found, their effect

on the overall flowfield can be examined.

Thus the discrete Fourier transformation technique discussed above appears

to merit further examination as a tool to identify coherent large scale structure

in real flow systems. In the generated test cases the transformation methodidentifies the center very well. In the real flow cases, the success is not

as dramatic but still quite good.

70

-- - ~ ___ _____

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'04

15. Bevilaqua, P.M. and Lykoudis, P.S.: Mechanism of Entrainment in Turbulent

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York, 1960, pg. 400.

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23. Sawyer, R.A.: Design and Operation of a Low Speed Gust Tunnel, AGARD CP -

174, Wind Tunnel Design and Testing Techniques, London, UK, Oct. 1975.

24. Ham, N.D., Bauer, P.H. and Lawrence, T.L.: Wind Tunnel Generation of

Sinusoidal Lateral and Longitudinal Gusts by Circulation Control of

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25. Simons, J.M. and Platzer, M.F.: Experimental Investigation of Incompressible

Flow Past Airfoils with Oscillating Jet Flaps, J. Aircraft, Vol. 8, No. 8,

Aug. 1971, p. 587-592.

26. Viets, H.: High Frequency Gust Tunnel, AGARD Conference Proceedings No.

174 on Windtunnel Design and Testing Techniques, London, England Oct. 1975.

27. Simmons, J.M., Platzer, M.F. and Smith, T.C.: Velocity Measurements in an

Oscillating Plane Jet Issuing into a Moving Air Stream, J. Fluid Mechanics,

Vol. 84, part 1, 1978, pp. 33-53.

72

""~ ~ ~ ~ ~ 7Z= -= 71..-11 't '' - ' ': ... w ," " -- . - im" '

., _ .: ;_- . R .

28. Lin, C.C.: Motion in the Boundary Layer with a Rapidly Oscillating External

Flow, in the Proceedings of the Ninth International Congress on Applied

Mechanics, Vol. 4, p. 155, Elsevier, Inc., Amsterdam, 1957.

29. McCormack, P.D., Cochran, D. and Crane, L.: Periodic Vorticity and Its

Effect on Jet Mixing, Physics of Fluids, Vol. 9, No. 8, August 1966,

p. 1555.

30. Pai, S.I. and Hsieh, T.Y.: Linearized Theory of Three Dimensional Jet

Mixing With and Without Walls, J. Basic Engineering, Vol. 92, March

1970, pp. 93-100.

31. Schlichting, H.: Boundary Layer Theory, McGraw-Hill Inc., New York, 1968,

Chapter XV, p. 391.

32. McCormick, W.S.: Personal Communication, Wright State University, 1978.

33. Liepmann, H.W. and Roshko, A.: Elements of Gas Dynamics, Wiley, 1957.

34. Kendall, J.M.: The Turbulent Boundary Layer Over A Wall With Progressive

Surface Waves, J. Fluid Mechanics, Vol. 41, Part 2, 1970, pp. 259-281.

35. McCroskey, W.J.: Recent Developments in Dynamic Stall, Unsteady Aerodynamics,

R.B. Kinney, Ed., University of Arizona, 1975.

36. Kramer, M.: Die Zunahme des Maximalauftriebes von Tragflugeln bei plotzlicher

Anstellwinkelvergrosserung (Bdeneffeckt), Z. Flugtech. u. Motorluftshif,

Vol. 23, 1932, pp. 185-189, (also NACA T.M. 678, 1932.)

37a. McAllister, K.W. and Carr, L.W.: Water Tunnel Experiments on an Oscillating

Airfoil at Re - 21,000, NASA TM78446, March 1978.

37b. McCroskey, W.J.: Personal Communication, October, 1978.

38a. Keesee, J.E., Francis, M.S. and Lang, J.D.: Technique for Vorticity

Measurement in Unsteady Flow, AIAA Journal, Vol. 17, No. 4, April 1979.

38b. Keesee, J.E., Francis, M.S. Sparks, G.W., Jr. and Sisson, G.E.: Aerodynamic

Characteristics of an Unsteady Separated Flow, AIAA Journal, Vol. 17, No. 12,

Dec.. 1979, pp. 1332-1339.

39. Quinn, B.P.: Acoustic Wing Stall Delaying Device, United States Patent No.

3,774,867; November 1973.

73

40. Drewry, J.E.: Fluid Dynamic Characteristization of Sudden-Expansion Ramjet

Combustor Flowfields, AIAA Journal, Vol. 16, April 1978, pp. 313-319.

41. Craig, R.R., Drewry, J.E. and Stull, F.D.: Coaxial Dump Combustor

Investigations, AIAA Paper No. 78-1107, 1978.

42. Edelman, R.B. and Harsha, P.T.: Application of Modular Modeling to

Ramjet Performance Preditions, AIAA Paper 78-944, AIAA/SAE 14th Joint

Propulsion Conference, July 1978.

43. Viets, H. and Drewry, J.E.: Quantitative Prediction of Dump Combustor

Flowfields, AIAA Paper 79-1481, AIAA Fluid and Plasma Dynamics Meeting,

Williamsburg, Va., July 1979.

44. Choudhury, P.R. and Gerstein, M.: Turbulent Vortex Flame Stability and

Spreading with Gas Jet Impringment, AFOSR Contractors Meeting on Air-

Breathing Combustion Dynamics, Dayton, Ohio, October 1978.

45. Anon: The Pulse-Combustion Furnace, GRI Digest, Vol. 1, No. 2, June 1978

(Published by the Gas Research Institute, Chicago, Illinois).

46. Rose, W.G.: A Swirling Round Turbulent Jet. 1 - Mean Flow Measurements,

Journal of Applied Mechanics, December 1962, pp. 615-625.

47. Stull, F.D., and Velkoff, H.R.: Effects of Transverse Ribs on Pressure

Recovery in Two Dimensional Subsonic Diffusers, AIAA Paper No. 72 - 1141,

Nov. 1972.

48. Haight, C.H. and O'Donnell, R.M.: Experimental Mating of Trapped Vortex

Diffusers with Large Area Ratio Thrust Augmentors, U.S. Air Force Aerospace

Research Laboratories Report TR 74-0115, Sept. 1974.

49. Stenning, A.H. and Schachenmann, A.A.: Oscillatory Flow Phenomena in

Diffusers at Low Reynolds Numbers, ASME Paper No. 73-FE-14, 1973.

50. Schachenmann, A. and Rockwell, D.O.: Prediction of Diffuser Core Flow

Fluctuations Caused by Oscillating Turbulent Flow, J. Aircraft, Vol. 15,

No. 6, June 1975.

51. Papaillou, D.D. and Lykondis, P.S.: Turbulent Vortex Streets and the

Mechanism of Entrainment, J.F.M., Vol. 62, 1974, pp. 11-31.

52. Quinn, B.: Compact Ejector Thrust Augmentation, J. Aircraft, Vol. 10,

No. 8, August 1973, pp. 481-486.

74

53. Bevllaqua, P.M. and Toms, H.L., Jr.: A Comparison Test of the Hypermixing

Nozzle, U.S.A.F. Aerospace Research Laboratories Report TR-74-0006, January

1974.

54. Theisen, J.G.: A New Turbulent Boundary Layer Separation Criterion Based

on Flow Dynamics, Lockheed Georgia Company, Report LG78ERO007, March 1978.

55. Walker, J.D.A. and Abbott, D.E.: Implications of the Structure of the

Viscous Wall Layer, Turbulence in Internal Flows, (Murthy, Ed.),

Hemisphere, 1977.

56. Lugt, H.: The Dilemma of Defining a Vortex, in Recent Developments in

Theoretical and Experimental Fluid Mechanics, Muller, Roesner and

Schmidt (eds.), Springer-Verlag, Berlin-Heidelberg, 1979.

75

Portions of the present paper have been published in the following papers:

1. Viets, H. and Piatt, M.: Linearized Unsteady Jet Analysis, Proceedings

of the NASA-Air Force-Navy Workshop on Thrust Augmenting Ejectors,

Moffett Field, California, NASA CP-2093, June 1978.

2. Viets, H., Piatt, M., and Ball, M.: Unsteady Wing Boundary Layer

Energization, Proceedings of the U.S.A.-Germany Data Exchange Meeting,

Meersburg, West Germany, April 1979 (also AIAA Atmospheric Flight

Mechanics Meeting, Paper No. 79-1631, Boulder, Colo., August 1979).

3. Viets, H., Piatt, M. and Ball, M.: Boundary Layer Control by Unsteady

Vortex Generation, Proceedings of the Symposium on the Aerodynamics

of Transportation, June 1979, Published by the ASME. Also Journal of

Industrial Aerodynamics, Spring 1981, In Press.

4. Viets, H. and Piatt, M.: Induced Unsteady Flow in A Dump Combustor,

(with M. Piatt), Proceedings of the 7th International Colloquium on

Gasdynamics of Explosions and Reactive Systems, Gottingen, Germany

August 1979. Also AIAA Progress in Aeronautics and Astronautics

Series. In Press.

5. Piatt, M. and Viets, H.: Conditioned Sampling in an Unsteady Jet,

AIAA Paper No. 79-1857, AIAA Aircraft Systems and Technology Meeting,

New York, August 1979.

6. Viets, H.: Coherent Structures in Time Dependent Flow, - Proceedings

of the NATO/AGARD Specialists Meeting on Turbulent Boundary Layers,

The Hague, Netherlands, September 1979.

7. Viets, H., Ball, M. and Piatt, M.: Experiments in a Subscale Pilot

Gust Tunnel, AIAA Paper No. 80-0453, Aerodynamic Testing Conference,

Colorado Springs, Colo., March 1980. Also AIAA Journal, Spring 1981,

In Press.

8. Viets, H., Piatt, M. and Ball, M.: Forced Vortices Near a Wall, -

Proceedings of the U.S.-Germany Data Exchange Meeting, U.S. Naval

Academy, Annapolis, Md., April 1980. Also AIAA Paper No. 81-0256,

Aerospace Sciences Meeting, St. Louis, Mo., Jan. 1981.

76

9. Bethke, R.J. and Viets, H.: Data Analysis to Identify Coherent Flow

Structures, AIAA Paper No. 80-1561, AIAA Atmospheric Flight Mechanics

Conference, Danvers, Mass., Aug. 1980.

10. Viets, H., Ball, M. and Bougini, D.: Large Scale Structures in Driven

Unsteady Diffuser Flows: Proceedings of the International Flow

Visualization Symposium, Ruhr University, Bochum, Germany, Sept. 1980.

11. Viets, H., Ball, M., and Bougine, D.: Performance of Forced Unsteady

Diffusers, AIAA Paper No. 0154, Aerospace Sciences Meeting, St. Louis,

Mo., Jan. 1981.

77 -

Table 1. Maximum and Average Streamwise TipSpeeds Relative to Freestream forthe Present Geometry and a NominalVelocity of 123.5 ft/sec.

Vrel Vrelois max VT-s av.

1000 1.026 1.017

-1000 .974 .983

2500 1.066 1.042

-2500 .934 .958

4000 1.106 1.067

-4000 .894 .933

5000 1.132 1.084

-5000 .868 .916

78

Table2

Re (xlO 4~

Fi gure RP Re VeHNo. RMVrel(m/sec) Vrlv e - u

4 3000 23.60 2.03 4.02

5 -3000 -.42 -.03 .015

6 2000 19.61 1.69 3.35

7 -2000 3.64 .31 .61

8 1000 15.61 1.34 2.65

9 -1000 7.63 .66 1.31

79

TABLE 3.

n

0 1 2 3 4 5 6

0 -- 0 0 0 0 0 0

1 -1.571 -.786 -.374 -.133 -.064 -.765 -.413

2 -1.571 -1.197 -.786 -.375 -.244 -.667 -.672

m 3 -1.571 -1.438 -1.196 -.786 -.505 -.549 -.709

4 -1.571 -1.507 -1.327 -1.066 -.785 -.536 -.450

5 -1.571 -.806 -.904 -1.022 -1.035 -.785 -.317

6 -1.571 -1.158 -.899 -.862 -1.121 -1.254 -.785

Table 3. Spectrum angles for the case of a single vortex at the axis of thephysical plane and turning in the counter-clockwise direction asshown in Figure 113a.

80

I!

TABLE 4.

n

0 1 2 3 4 5 6

0 -- 1.765 -2.753 -.989 .777 2.541 -1.977

1 1.182 -2.551 .374 1.632 -2.817 -1.753 .363

2 -2.348 -.209 1.968 -2.140 -.244 1.098 2.857

m 3 .406 2.304 -1.973 .203 2.248 -2.314 -.709

4 -3.124 -1.295 .650 2.675 -1.562 .452 2.303

5 -.371 2.159 -2.457 -.810 .942 2.956 -1.094

6 2.383 -1.723 .302 2.103 -2.674 -1.042 1.191

Table 4. Spectrum angles for the case of a single vortex shifted from theaxis of the physical plane to a position of P = 50, Q = 64 andturning in the counter-clockwise direction as shown in Figure 114a.

81

-_:7

TABLE 5.

n

0 1 2 3 4 5 60 -- 0.0 0.0 0.0 0.0 0.0 0.0

1 -1.571 -.786 -.299 .179 2.480 -2.609 -.614

2 -1.571 -1.272 -.786 .240 1.047 -1.439 -1.006

m 3 -1.571 1.749 -1.811 -.786 -.151 -.492 -1.125

4 1.571 2.232 -2.619 -1.420 -.785 -.183 .314

5 1.571 1.039 -.132 -1.079 -1.388 -.785 .056

6 -1.571 -.958 -.565 -.446 -1.885 -1.627 -.785

Table 5. Spectrum angles for the case of a constant magnitude velocityrotational flow.

82

AD-AIO 291 WRIGHT STATE UNIV DAYTON OHIO F/G 20/4PROBLEMS IN FORCED UNSTEADY FLUID MECHANICS.(U)NOV 81 H VIETS. M PIATT. M BALL, R J BETHKE AFOSR-78-3525

UNCLASSIFIED AFWAL-TM-81-148-FIMM Mt.

m mmmmmu[loommiIBBhhlnllBEBBBI EEEEIE~I/HEEEEEEEE0iniU

112.8 1 2 .5

11111L2 111111.

MICROCOPY RESOLUTION TEST CHART

TABLE 6.

n

0 1 2 3 4 5 60 -- 1.765 -2.753 -.989 .777 2.541 -1.977

1 1.285 -2.551 -.374 1.632 -2.817 -1.753 .3632 1.825 -.209 1.968 -2.140 -.244 1.098 2.857

m 3 1.294 2.304 -1.973 .203 2.248 -2.314 -.7094 1.748 -1.295 .650 2.675 -1.562 .452 2.3035 1.657 2.159 -2.457 -.810 .942 2.956 -1.0946 1.822 -1.723 .302 2.103 -2.674 -1.042 1.191

Table 6. Spectrum angles for the case of a vortex convected in a parabolic flowvarying in the N, direction as shown in Figure 116a.

83

TABLE 7.

n

0 1 2 3 4 5 6

0 0 0 0 0 0 0 0

1 1.301 0 0 0 0 0 0

2 1.485 0 0 0 0 0 0

m 3 1.572 0 0 0 0 0 0

4 1.634 0 0 0 0 0 0

5 1.685 0 0 0 0 0 0

6 1.731 0 0 0 0 0 0

Table 7. Spectrum angles for a parabolic flow varying in the N, direction as

shown in Figure 116b.

84

TABLE 8.

n

0 1 2 3 4

0 .081 -2.955 -2.230 -1.544 -.919

1 2.691 .049 1.234 1.463 2.260

2 -2.294 3.119 2.802 2.615 -2.993

m 3 -1.483 -2.380 -1.843 -2.464 -.415

4 1.798 -.675 -1.406 -.985 .761

5 -3.012 .227 .471 -1.193 -1.437

6 -1.545 -2.994 2.157 .683 .848

Table 8. Spectrum angles for the case of the instantaneousstructure of an oscillating jet, transformed fromFigure 117.

85

TABLE 9.

n

0 1 2 30 0.0/-- 3172.0/-1.236 3820.1/ .671 2183.6/2.5771 2965.5/-1.571 3163.1/1.120 2748.9/-2.845 1432.1/-.698

2 2837.3/1.571 2131.9/-2.433 1199.6/-.115 512.4/2.2013 945.8/-1.571 544.4/.468 174.3/2.616 16.3/1.791

Magnitude/Angle

Table 9. Partial magnitude/phase angle matrix produced by the transformationof the two-vortex velocity field of Figure 118.

86

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Ficure 4. Experimiental Setup

90

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0 U

0-.1-2 .25 .50 5r_0 uo

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Figure 5a. Time averaged velocity measurements in theoscillating jet, Uo=43 m/sec, w=12 Hz.

91

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0 0

Q000 4-141

0 ~ O N . 4

-I. 0

:3a

97a

ix ix

0

000

a GoUJ W

m- 0 4 C 0 -

o-J _

00 000 N -

0~ 0

0I 00

S-

4-)

o .0

4JUI:r

44-4NM

0~3I Z

0 0)

N 10

98

Signal Amplifier Band Zero crossing

SH pass filter detecortriggering .

hot wire .'Variableprobe .- " phase shifter

X hot wire Suppressionprobe fle

sign s

Bridge Bridge pi

Amplifier Amplifier igger

Suppression Suppression Differentiatorfilter filter

Linearizer Linearizer

Logic Input

Sum & Difference

D.C. Filter--- --- -- dAmplifier Amplifier " Sample & Hold

(Average) X-X (Instantaneous)

Potentiometer for go X-Y Plotterprobe position Y

Figure 9. Schematic of the electronic circuitry employedto conditionally sample the unsteady jet flowfield.

99

09,360[

o90° 270

1800

Fig. 10

Figure 10. Definition of the jet phase anglein terms of jet orientation.

100

C\.)

4).

Ix 064-0

C: mo*

Q 0~

4- 0

r- t

I.-

C.o 0-

:D

60

101

6L~

06

CL

0O

060

S4n

102.

0

* I

N4J

L-

103

0.L

Ix

06

43

104

ixN

0

4-

a,>,

(A

4--00

4--

IMI04S-

EL4-

00

Ix

105

8-

-x4 goo

-2 5 10 15 20 25 307

-4Fig. 12 b

Figure 12b. Transverse location of the maximum streaitiseI velocity with distance downstream, e=900.

106

Y/D

.50 1.0

0 Y/D

up down .250

Fig. 13a

Figure 13a. Instantaneous velocity profiles in theoscillating Jet at a frequency f=12 Hzand a phase angle e=180*.

107

0I

C

06.

4-3-

0~0

- 100

06)

0

4-I

0

L--

0

0'4-

vo

4-

J-

0 1

0Cj

i4--

Ix.

Ix

8

080

2

-41A

Fig. 14 b.Figure 14b. Transverse location of the m~aximum streanmiise

velocity with distance downstream, e=180*.

ix

CD

0~

4--

Ix0

'4-

0.

oi 0

d,III

IIIIII~lII1...........-

'4--

0

ix CE0

0

(\j IX

Ix

112

1.01 f< Hz

Ymax 01/2 D 1 0

1.0Figure 15b. Transverse location of the maximum

streaise velocity with distance down-stream, 6-270*.

1.0-0-0 a 90*

U max ..... 270*U0

.... TO.

f: 12 Hz

0 10 20 30 40

Figure 16a. Instantaneous velocity decay for variousphase angles and a frequency f-12 Hz.

113

1.0

---- 0 e 9o*

Umax ... A e 270*

U0

f :18Hz

o I I I0 10 20 30 40

Figure 16b. Instantaneous velocity decay for variousphase angles and a frequency f-18 Hz.

-- , I I ' I 1 ' I

34 I,~II30 !"A26 /

22 / I

Is i

14 tt14 i . , i I, I I i i I I I

-60 -40 -20 0 20 40 607y.nu(mm)

Figure 17. Typical velocity profiles from Simons,Platzer and Smith, Reference 5.

114

4- 4.)

0 t5-

4-) C%)

C)

>f 4-)

4.)

4-

o

In,0.

115

W W

a)a

I- Y

al ,,1

402J

* A. d116

C

Ix

NNj

IC

(o44

0 W

4

'00

0N

47/D

117

1110111

--, ,,i -,- -,- --' (,VU 18 H a

l . i ( = 2700

/ / Instantaneous# / / jjet.

centerline

I I I I

14 16 18 20 22 X

Figure 20b. Coherent structure of the jetseen in a moving coordinatesystem.

ii

r

118

A...... = 12Hz

0=90

0 90

~ ) . . ... .. .

0 180

*.. %

PS' ~v

0 10 20 30

Fiur 21k. Anticipate vote loain 0ae nfoviulzto reuls

~$%:~. 119

C) I-

0) I0

Cn0 4-

M 04 ,. 4- OD,

C4.) 0

Eu

I I 5 '4---

4- EScm

0

120~

0)

u (0 AC 0A

=3o0 0

LL.

1N21

Ix

(%J~j

00C~j 00I

14. C>

U))

k>

122

IA

0) I.

U) C\J 0

Cg

0

4-0

4)

4--

C4

L.

$112/

0N

'U U)CX) 4-

0 o C*C

II(D CD

' 4-0M 4-

0.C

>04 J.C

w c

124

Ix

ODN .- 1'

0

4-a4--

'4-)

4-

U U

.8

LL-

125

f=18 Hz0=2700

~~~1.0, i

Um .8--20 30

.2.0 30 40X0 10 20 30 40

Figure 25. Effect of the vortex structure on the instantaneousjet velocity decay.

126

SFLOW

OPENED

Figure 26. Schematic of mechanically controlled,fluidically activated nozzle.

TUNNEL ROOFJI///////1/!A

TUNNEL FLOW - TEST SECTION

TUNNEL FLOOR A1

Figure 27. Schematic of jet controlled gust tunnel.

127

... . +

FLOW~

.0cm

3.56 cm -

cm. 18cm

2.54 cm 305 cm

Figure 28. Geometry of the experimental subscalepilot gust tunnel.

128

* I-

60 Hz, 0* Phase

600 Hz, 180° Phase

Figure 29. Flow visualization of the in-phase configurationin the up and down orientations.

I 129r IF I

Signal _w Amplifier Band Zero crossingpass filter detector

Variable

. phase shifter

hot wire Suppressionprobe ffilter

t signals f

Bridge Bridge Amplifier

SchmittAmplifier Amplifier trigger

Suppression Suppression Differentiator

filter filter

Linearizer Linearizer

Logic InputSSum & Difference

u v ---------

SD.C. Filter

Amplifier Amplifier Sample & Hold

(Average) X (Instantaneous)

SPotentiom eter for - Pl t e:,probe position y

Figure 30. Schematic of conditional sampling electronics.

130

Y~bl X-20

20

0-.25 .5o u/U .03u

20-

30 down up'

Figure 31. Flowfield at X = 20 for the in-phaseconfiguration in the upward orientation.

30

20

'0. .03

20

S"30 down up

Figure 32. Flowyield at X = 20 for thein phase configuration in thedownward orientation.

131

Ix

O

4-

0 0

w 0

000

TO 4-'4-o to

1321

'0 1

132

1I5

J0 time

htme

v X=x -25

Vrv =30

- hme

Figure 34. Variation of the centerline transversevelocities with time at several stream-wise positions.

133

r w

~30--,

20"

0 .25 5 u/u-

10

20"

30 "2 300 down up

Figure 35. Flowfield at X = 20 for the outof phase configuration and aninward orientation.

030 -

20--

0-~ .2 .50 U1 .03U

20-

down UP

Figure 36. Flowfield at X = 20 for the outof phase configuration and anoutward orientation.

134

X=20

X=25

UA t________________________X=30time

Figure 37. Variation of the centerline streamwisevelocities with time at several stream-wise positions.

135

30.5 m/sec (100 ft/sec)

27532.5 3 425 -X

475

Figure 38. Streamwise velocitieL at various positions witha 450 phase lag between the nozzles and theupper nozzle in the upward orientation.

136

30.5 r/ sec (100 ft/1sec)

17. 2.5275 32.5 375 425 47.

425

Figure 39. Same nozzle configuration as Figure 13 but withthe upper nozzle in the downward orientation.

137

L m. . -. * . . . . .

QC)

oL 00 C-

f 'cI~ C1L

Sf-

C- 4-M

a >

C --

'0

4J

CO

0>

.9-

13- 4

C0CC

N

C),

C

C) 5

(0CD

-cL

0

Cj

C)

139

Figure 41. Schematic of the vibrated Jet studied by McCromack,Cochran and Crane.

91

.. 6. 1 !2

9.1 IVA-ANN .

mm" ~ .

Vj Oa ;

Figure~~~~~~~~'A 42%lpigjtwt nua ~~vraina h

:~i1~did y Vet e a. ad laze

140

ZN-.-

'X

Fiur 4.Je wt time deedn mas flo su.ied

-AM-

Jet Velocitu~t) u-=u(t)

initial downstream

Figure 44. Initial and downstream velocity profiles.

141

-FLOW

Figure 45. Fluidically Controlled Jet Nozzle Design.

142

I (0

N VC4C

CE) X 4Jco I

C

0 *

0 4J*

C )M

E000

tt

U 0 to 0 I)0

(3/r, = SBWPNJ.4 GIZZON/fP!M MUH XZ

143

y

Viee

x

period =wx

Figure 47. Flow over a way wall

144

a

a=a, +a" sin, w t

Figure 48. Geometry arnd Flowfleld of an Oscillating Airfoil.

145

~. . -4-- 2

0- S-

J-

.04EC).

0N

prPall

<9

.0 4

4LU'G

tit0.

-4'~,.. v ~

1liI

41)

Cp

147)

L .953 ROTOR

-a-2.44Rotor axis

737--- Pressure tap location

AIROI 2.21.356

7.87 cm-i

12.50 cm

Figure 51. Airfoil and Rotor Geometry.

148

jj UM-M =

PLEXIGLAS

END WALLS

Figure 52. Airfoil Mounted for Low SpeedWind Tunnel.

149

Rotor location

Figure 53. Vortex Structure Behind the Rotor on a Flat Plate.

150

a, (u-()

!

I

be U 4

Figure 54. Flow Visualization of the Flow Structure at= 200.

151

a=200

-~--O rpma- -- = 2 4 0 0 rpm

oYL=20 °

.... (U= 180 gorm...... _&-=2400 rpm

b.-

Figure 55. Effect of the Rotor Speed on the

Streamline pattern over the Airfoil.

152

a=20 to=1000

Figure 56. Instantaneous Vortex Structure on the Airfoilfor c 20, 1000 rpm.

153

P-Pt 1.4 -I l(P-Ps) 1.3

1.1 015 --

00

1.0. I , I0 2 6 10 14 18 oXI10

rpM

P-fs dli-AA IAi

(P-Pf) 1.2-AA -- i£2.1.1 - , , a= 18" I F1.01 & 1 i ,

10A 14 18 &XIo

.02 6 10 14 18 wXlOO

~ rpm

Figure 57. Pressure Variation with Rotor Speed forThree Angles of Attack.

154

P ta l

A**

1.0F

A Maximum with rotor activated

0S0 10 20 30 a (Degrees)

Figure 58. Pressure Variation with Angle of Attackwith/without Activated Rotor.

155

V4.635 CM

Figure 59a. Unsteady Ramp Flow configuration

RS 3p I05C

Figure 59b. Tunnel Geomnetry

1 56

L Ppf..2, 20*.. 5'pV2' .,1,

0- 1.0 1.5 2.0

/ xW(rpm)I 0o

22500 ---

-3/

-.4, /1

Figure 60. Pressure Distribution on the Ramp for8=200.

157

pI s..2 e 28° :.pv2 ., ,..1 <-

.5. _ 2.0

-2~~~ .-_ (rpm)

001000 --2500 --4000 A

1*5000 L-.4,, I .. .. .

Figure 61. Pressure Distribution on the Ramp for -28*

158

.35

0..

0. 00,w (rpm)

-2 p 1000 0 -2500 K4000A

5000 .....

Figure 62. Pressure Distribution on the Ramp, for=300.

159

-o

I0

N

*0

S..a.4-

_________________________________ LL

0DU)0S.-S

0

I-

(Y)to

0I5-

U)

U-

0 0

CL

Im-

0.

4J CL

04

W .

c u

L.

1610

'IIV

162~

VELOCITY

VORTEX

oEND CENTER

CROSS SECTIONS

Figure 65. Schematic of a three dimensional rotorgeometry (Tapered rotor).

163

-~ ..--- -.--- -~ - -.

E0.

0.0 00

009 Co

O-3U .~n .

4J -

o .4- E-'

0,I '-0 -c

O O 00O

0U 000- 3C 1

EC

o 0.

) z

164

• . .. ... . 2 7 - " , .*.: - 2 . • -' - - * - -E

EE0. 0.o 0o 0

U)

Ln

00

o 00

4r -

LiI

o 0o 0

LOj U)

165

.3

P-PfS .2-12

01

Q .5 1. E 2.0

-.1

-.2 1

0=28-. 3-e = 280

TAPERED ROTOR

W (R PM)

10000

-1000U

Figure 68. Pressure rise down the ramp for t1000 rpm and a tapered rotor.

166

-No

.3

P-Pfs .2'/2 PvZ

.5 1. 2.00* b

-1L-. 2 k

-.3 :28°

TAPERED ROTOR-.4 w (R PM)

-.5 5000 N

-5000-. 6

= Figure 69. Pressure rise down the ramp for ±5000 rpmand a tapered rotor.

167

... .. " ", _ "2 .....

060

0

*o4- S-

I--o -0NCL C M

E-I

a.S I-

1689

o 1..

o 0-

0 0

0I 3

160

0 L

a

-

0

D 4)L'4-

170

d Rx/h

.381 cm

.478cm

Figure 73. Experimental Geometry and Rotor Flowfield.

171

04

W) 2500 rpm

_________w =4 000 rpm

----.- - - -. -4

0p

Figure 75. Instantaneous Streaklines for0. ,i 1/3.

173

b.c =2500rpm

0 48

C. w =2500rpm

Figure 76. streaklineS at Three Different Instants,

w*2500 rpm. 1/3.

174

048co =5000rpm

Figure 77. Streaklines for w =5000 rpm, Fl=1/3.

175

013

to 2500rpm

O( =5000rpm

Figure 78. streamline Shapes for various Rotor speeds,

176

0 2 3

(=2500rpm

0 1 2 3 x

w =5000rpm

0 1 2 3 R

Figure 79. streaklines for Various Rotor Speeds, h=1

177

2

..p.. S.p112D V ..

• - Ih= 113

I )(rpm)

0 0 --10 00o 1 --

2500 K-* 1 4000 A .

. 5000 i .....

Figure 80. Pressure Distribution Downstream of the Dump Station;= 1/3, Various Rotor Speeds.

178

AD-AlO 291 WRIGH4T STATE UNIV DAYTON OHIO0 F/S 20/4PROBLEMS IN FORCED UNSTEADY FLUID RECHANICS.CU)NOV al H VIETS, M PIATT. M BALL, R J BETHKE AFOSR78-3525

UNCLASSIFIED AFWAL-TM-81-1'I-FIMM MA.uuua2uu

momWUEEUHIW

IIIII c 'nil '-moo 111122III I I-I~13.6

11111.2 1.4_ UT IIOTS

MICROCOPY RESOLUTION TEST CHART

.2-co(rpm)

_____S 1000 0 -**

-/2V 2 2500 '--.1 4000 "--

o I .. , /I

*.-1,-I 1

, t £..,. _ , .' 1J.(h =210

-. 2,

Figure 81. Pressure Distributions Downstream of theDump Station; F = 2/3, Various Rotor Speeds.

179

--. . . .. ".] ' ' 'i- ?,..' "f '" " ,r'. ,,',-a. " • ,. ,*, /. , ,- -""""" -'- " .- " - ..'-- ' ..- -.. . . [

.20

.15 w(rpm) 0 -0 0

1000 0 -- h=1.10 2500 - - -

P-pf.j 4000 A ....

1/2p 5000 .......

0 '12 3_.

-. 05-

-.1-.15 \

-. 20 '

Figure 82. Pressure Distributions Downstream of the DumpStation; Ii = 1, Various Rotor Speeds.

180

'cJ8 0

000':10 00 .

0 0

CVU)

h0 8

8n 0

0no c60( C4

1814.

* .2

. F I=113

112loV 2 +-.05

* .15 Q withdrawn

tripped

-.3Figure 84. Effect of Rotor Geometry as a Passive Trip.

182

(a) In Phase

(b) Out of Phase 17Figure 85. In phase and out of phase rotor orientations.

183

4-

4- [

00

0)

1840

Figure 87. Multiple vortices produced in the diffuser by

increasing the speed of the rotor.

185

lu J.

4-)

0

GJ >

o -

/ O a. 4-

S 0 4J

C- CA 0

4- 0) 4*v0 -

0.' 4-e

00 0

co CU~

t. t t-

I 0 i~) 186

--- 0go,

Figure 89. Longer exposure streamline photographs forZe -.30 . (a). Separation at the bottomfor u - 0 (b). Weaker separation at the topfor u - 11.84 (both in phase)

187

4 0 0 0.3 00A&°°

0 0 o00.2 0P1 o§ 90 0 290

0 W0 0

-.2 2 810.93 29-160= 14.44 Out of Phase=17.96

Figure 90. Pressure rise through the diffuser for 2e=16and various rotor speeds, out of phase.

I8

0OO0

..

0 0

-. 2 0 W- t

0 =1o 2e_24o

S = 14302 Out of Phase

:= 17.80Figure 91. Pressure rise for larger angle diffuser,

20 = 240, out of phase.

189

x 0

0

.3-

.2 A,1 O

09 0

-. I 0-. 1 x 0 8g5

0 v = 0 +0 20=300= 13.14 Out of Phase0 16.23

A = 20.35

Figure 92. Pressure rise for 20 = 30°, out of phase.

190

!w

0 20

a0 =O + 2e = 24P0 11.23 I n Phase

=14.83

=18.53

Figure 93. Diffuser performance for rotors set in phaseand 2e =240, in phase rotors.

191

-- ... .. ... .. ... . .. . . -.. . .. : . .: .. ... t~ ll~~i r. =. . .... . T. .. _ =.. = -- , ..-.'.-.,

.3

P.2 0 o

~0

00

i _ o2e -3ooo 1WO In Phaseo =11.840 =15.87

= 20.18

Figure 94. In phase pressure rise for 2e 300, androtors in phase.

192

20 240 W 11.231n Phase

Figure 95. Streakline photographs of the diffuser flowat different phase positions with superimposedInstantaneous velocity profiles.

193

200 30 PW=90.1

Out of Phase

Figure 96. Streakilne photographs for a larger diffuser angleand for the out of phase rotor orientation.

194

Figure 97. The presence of a counter-clockwisevortex near the upper wall or aclockwise vortex near the lower wallleads to instantaneous velocity changesin the streamv)se (u') and transverse

) directions.

71 195

Y y

0 (P=t80 0 .05 .10

o In Phase -- -4U 0 -+H

W= 11.23

E) =24*

Figure 98. Velocity difference between the presence ofa vortex pair (~=1800) and no vortex(0 900).

196

o(P=9O0 .70 90 .050- ()= 270~ Ui 0. -+V

Out of PhaseW 13.14

5 ) e300*<

0 - 270o I- I- 0 0- V

Figure 99. The velocity changes due to the presence of asingle vortex in the out of phase condition.The profiles are those in Figure 96 (b) and(d).

197

0*

*. ~

~ ~l~*. L

8..* *. * 4.)

** 0.*e .~IJ~5 *~*'~ I.

* ~ &4***.) I..'

.. *4. S - 0*4,*.*.~ ~ *~* U

v.i.::;~ *~, 0* .,:.~*... *. 3 t..

.0

@1* 4.)

~'

3**~ ***.**** * ** 0**. is. * *. *. .* *. -

* *** S. ** *4~.* *...* *.*

* * ** *.t**** *. ***.t** **.c **** * .

* 0 *. .0* * a,*.* **. * ... I * *

* **'* *0* ***~-- 0* *JS~ * L.

**~* ~ *

* .0** * * 4)

* . * * .S * 4.)

* ** S *0 * I.-

0U

4.)0Ea,0

0

a,o -

0)

U-

k

198

b

CO + 3000 rpm

Figure 101. Flow visualization of vortex structureproduced by the vortex generator with- 3000 rpm.

199

.. . .. . . .,*

7 L

W = -3000 rpm

Figure 102. Flow visualization of vortex structure produced

by the vortex generator with w = -3000 rpm.

200

C2000 rpm

Figure 103. Flow visualization of vortex structureproduced by the vortex generator with

= 2000 rpm.

201

i-

C0-2000 rpm

Figure 104. Flow visualization of vortex structureproduced by the vortex generator with

=-2000 rpm.

202

CO= + 1000 rpm

Figure 105. Flow visualization of vortex structureproduced by the vortex generator with

=1000 rpm.

203

p--7-

W W

CO=- 1000 rpm

Figure 106. Flow visualization of vortex structureproduced by the vortex generator with

-1000 rpm.

204

H~ot WireAmlfe

AmlfirAmplifier Ban Sae cr odn

Potntomte fitoreeco

otter

rwobe pScitiontFigurfer 10.Shmtic fie codtoetapqaratus.

Sup re sin up re sio Dff205ito

- ~ ~ ile filter- r1~~~

Ix

41

c C

C-)

4)

LL

00-o

206

-- OW---

SI p <

5 6 7 8 9 /0 e= 0*l" . (,IW=3800 rpm

Figure 108b. Identification of a vortex structure in a reference' frame moving at 11.5 m/sec.

207

IXI

CD

4.5

44' \ \\ I 44

C) ~L

20

4JJ

'4-

4J

I' F ~\ '~ ~4)

209a

Lo

ty0

0* 4)

N WA-

21a0

04 V o At.

*%

rz _0_0, I I lI1- 11 1

e 120/

Figure 109d. Identification of a vortex structure in theflowfield of Figure 109c.

211

0

I×I

4I -.

14 4)o

0111-

D CD4-E

21 0*3

k 3_

212

po so l

p. *. .p

U' U'A.

ap 'V

i'000

2 4 5

e=240*Figure 110b. identification of a vortex structure in the flowfield

of Figure 110a at R 4.5, y=2.0.

213

Ilk

9/0 II 12 13 14e =240*

Figure 110c. Identification of a vortex structure in the flowfield

of Figure 110a at x =13.0, y=5.75.

214

C)o

0 IUD

Vt--

A0

Q" S--I) -

U.-

215

5

IIIII~ I5

Co

0

0

)

4.-

C)~

216-

* 41.

• * -22 2 1 22 :: . . 4

' *.. . . 't *, t T " . , 1 1 11 1 1 I I I 4o , 4, , , ,

. . . . . . . . . . . . ..... . . . .. . . .- - - - - - - - - - . . . . ..... .,

* i, lfI~lIIII/// I//lll\l~l 4444'~~'~~''~ %t4 \ % %4 I

4i44r4 13. Spatial vortx0exst

% 7

% % - - - - - - -

I %4%4I444 S- --- .- - -I

44%4444 -- -- -- ---

- - - -- - -- - - -- - - -- - -- - - -- -- - - - - - -

Figure 113a. Spatial vortex existing on the axis.

217

- - -. . -

- n

real

imaginary

Figure 113b. Transformation of the vortex of Figure 113a.

218

10-45

.....• . . : :::: ::: ::::..........::::" ii ii ii.. .. ............. ...*~ %.

77,, . fP -4 5 N1=4A A.. . . .. . . .A.S.. .A . . . .. . . .

%5 %S %'' %S * 55 5

ii iiii#....*\\\ \ t S t S

% % '*a I I 11111 a .,

* ism Ba 11 i tl \ \\ -' sl# llI/ Iij I i,..

. . . . .. . . . . . - ----.

a .. . . . .. . .. .~ . .% . . . .

2 4 i . .\ .. %.%/l ...

Figure 114a. Vortex shifted to an off axis location.Center shifted down by 50 units and rightby 64 units from the upper left data point.

219

--S , s s , ,,,*545 St .S * - - - - - - SS 5 5.5 eti

1(0,2) 0(0,2) - 2vt 2Q

2122N

~2n~(1,0 o 1,0 1 N -

S(2,0) =(b o (2 ,0 ) - 27 2P

0) (2,2) = 0o(2,2) - 2n P - 2Q0N, N2

Figure 114b. Schematic of phase angle shift.

220

\\\ ow 1. I

huh II' , 44444i

Figure 115. Rotational flow with a constant magnitudevelocity.

221

C a

cicooC~C

L

uu

too

0.

X410

-

l444444~~\\ 0

L.-

11999?14 a 4222

4. 4. . 4. . 4. 4. 4. 4.. 4. 4 . 4 . 4 . 4 .. .4

4. 4. 4. 4. . 4. 4. 4. 4. 4. 4. 4 .4 .4 .4 .

Fiur 116c. .4 . .. 44 4.Fl4.el in the moin coordinate.system

4. .4 4. 4 4 44. 4 4 . 4 4 4 4 . 4. 4 .223. .4 .

-- pp,

-A

-- p

Fiur 117 Intnaeu eoit tutr fa

osilain -t

-U

- 224

-4s -ql -4

, 1

/i / /

4

-4 k 's -

r~

. ,Fiur 18. Flw trctreina efrecefrm"i mvin wit th velcit at he oin

A A

4.. .a

_ 1

Fiue18.lwsrcuei eeec rm

moin wiI the.veocityat.th.poin

4? v v ~ . ~.~ A

4' V r 4 4

1 %IL . ,

INP t " Vp ~44

Figure 119. Generated velocity field containing twovortices.

226

______N 2

P2

Figure 120a. Schematic of two vortices in thephysical plane.

227

i! 27T nO, an*'m" en

a.nm R2n 0271V2

amn

N1

am.'no 2 m'P

N,

Figure 120b. Schematic of the transformed plane of vortexnumber I in Figure 120a showing magnitudes and phaseangle changes due to shift of vortex center location.

bnm - N2 h - N2

bmn271

MP2

271moP

Figure 120c. Schematic of the transformed plane of vortex number2 in Figure 120a, showing magnitudes and phase anglechanges due to shift of vortex center location.

228

1

Cj

229

ff 8-- m

k L

4-)

A~~~~4 4r_ ' a a 4% 4A I ~ 'a ' 'a a 'a 'a ' t v

230

0Ea-

E

-

00

* 4 4 # 4 4a ~ J t f >E0

* 4 44 4A4 f 4) -

*CA 4-)

4 44*4411w*

A,

ILL.

231*U.S.Qovernmont Printing office: 1931 - 559-005/4032